THE ADMINISTRATION is expanding its nationwide promotion of ride-sharing -- using car pools, van pools and mass transit instead of driving alone. Some of the missionary work needs to be done in the federal offices here where the end of free parking this Thursday has caused such loud complaints.President Carter has been firm about phasing out the parking perk to discourage solo commuting. But he has had trouble getting many agencies to do the rest of the job: helping employees with real transportation problems and actively encouraging ride-sharing in general.

One interesting example involves Vango, the pioneering van-pooling program run by the state of Maryland. Vango does not underwrite the vans; those who use them, currently about 700 people in 106 groups, pay lesing costs. But besides helping groups organize, the state corporation guarantees the leases and arranges crucial matters such as licensing and insurance coverage for the fleet. In short, it offers the sort of financial coordination that federal agencies, by law, cannot provide for their own employees.

How many federal offices and workers in Maryland use Vang's services? The National Security Agency has 36 Vango groups. The Social Security Administration in Baltimore has 24. But the vast array of agencies in and around Washington has only 12-- and two-thirds of those are at the Defense Mapping Agency (5) and the Geological Survey in Reston (3).

The numbers may be small, but the disparity is large. What casuses it? The key factor, according to a Vango spokesman, is that NAS and SSA have gotten organized. They have effective, continuing programs to explain the financial and energy-saving advantages of ride-sharing and get empolyees together in car pools as well as vans. This is the kind of positive effort that Mr. Carter asked all federal installations to start last spring. The Vango figures suggest how uneven the response has been. Now Mr. Carter is following his directive with an executive order. That should finally stir the laggards, especially at suburban agencies where mass transit is less available and pooling is the best way to cut commuting costs.