With all the speed of a sleepy snail, the banking industry is reacting to a problem that really makes its customers sore. When you deposit a check to your account, you may not be able to draw against it for several days.

The banks won't release the money until the check clears, as a precaution against check kiting. But the clearing system is unreasonably slow, and in the meantime the bank has your money to invest.

In recent hearings before the Senate Subcommittee on Consumer Affairs, Sen. Chris Dodd (D-Conn.) complained that most banks will not credit a personal check drawn on a local bank for three to four working days, and more than 10 days when the bank is out of state. Checks drawn on S&Ls and savings banks might take seven to 15 days to clear, and sometimes more.

No remedial legislation is in the hopper. But a staff member of the Senate Banking Committee told my associate, Virginia Wilson, that in this age of electronics, five days should be plenty long enough to clear a check. The American Bankers Association is proposing some solutions to the problem, but banks do so well with the present system that they haven't much incentive to act.

Some ideas on reducing delays in your own account:

1. Many people move to a new city, or change banks, and set up new accounts by writing a check on their old bank. Alas, they then can't touch their funds until the check clears.

To avoid this frustrating situation, visit the new bank and ask how to gain instant access to your money. Maybe the funds should be transferred from your old bank electronically. If you bring a check, maybe the new bank will telephone the old bank to be sure the check is good. You usually have to prearrange some sort of identification, to assure the new bank that you're not carrying stolen checks. Don't close your old bank account until your new one is fully functioning.

Many people move their bank deposits in the form of a certified bank check, assuming it to be as good as cash. Not so. Forgers can make such good copies that your new bank will usually put a hold on the certified check until it clears.

If you can't arrange for instant access to your funds at the new bank, take enough cash in the form of travelers checks to tide you over for the necessary number of days.

2. If you are a steady customer, your bank should let you draw against a paycheck or U.S. Treasury check immediately, if you ask. (But it might not let you draw against someone's personal check that you're depositing to your account.) Small banks are often more accommodating on these matters than big banks.

3. Have your college student keep his account in your home bank. You should then be able to switch money from your account directly into his, so he can draw on it right away. (If local merchants resist his out-of-town checks, however, he might be forced to use a bank in the college town.)

4. Many large corporations arrange with a particular bank to cash its paychecks without delay. Smaller companies could do this, too. The bank charges a small fee for the service.

5. Recipients of Social Security checks, railroad retirement, veterans benefits and some other federal checks may have their payments wired directly to their banks, so they aren't held up while the checks clear. Your own bank should, on request, let you cash a U.S. Treasury check immediately. But if the bank doesn't know you, it will put the usual hold on the check to be sure that it actually belongs to you. Some corporations also deposit checks directly in employe accounts.

6. Some banks let you draw on all checks immediately, provided that you put up other bank accounts as collateral. Say, for example, that you have a $10,000 six-month certificate, and the bank lets you cash someone's check for $1,000. If the check bounces, the bank could take $1,000 out of your certificate. If that means breaking into the certificate before maturity, you would have to pay a three-month interest penalty.

Banks should give you time to cover the bounced check before they take any money from a time deposit. Ask about their policy in advance.

7. Use an interest-paying checking account, if you meet the minimum-balance requirement and the fees aren't too high. Most institutions start crediting interest to your account as soon as the check is deposited, rather than waiting for it to clear. So although you cannot draw against the funds for a few days, you will at least be earning interest on them.

8. Banks can clear specific checks for you immediately, through their electronic system for transferring funds. For this service, they might charge $10 to $25 per check.