MILAN, JUNE 10 -- Police clashed with rowdy soccer fans in downtown Milan before today's World Cup match between West Germany and Yugoslavia. At least 23 people were injured and 36 taken into custody, police said.

Groups of soccer fans smashed windows of shops and cars along the street near Duomo cathedral square. Hundreds of riot police rushed to the area after reports of the confrontations between West German and Yugoslavian fans. Fans then began to hurl cans and bottles at authorities, police said.

A police spokesman said 15 fans and eight police officers were injured.

"Many had been drinking beer heavily," a police spokeswoman said.

Many fans took alcoholic beverages from home or bought alcohol the previous day to avoid the ban on selling alcohol on game days.

Meanwhile, Verona police reported that 13 West German supporters were arrested. Charges of violence and vandalism also were filed against 55 others following several Saturday night disturbances along Lake Garda, the Italian news agency ANSA reported. Englishmen Under Watch

In Cagliari, Sardinia, tensions eased as everyone wondered what had become of the English soccer fans. Twenty-four hours before England plays its opening match against Ireland, only small groups of barechested English fans were seen wandering the nearly deserted streets.

Police were out in force but no incidents were reported.

Street violence leading to the arrest of 14 English fans erupted Friday night, but by Saturday the English joined with the Irish and the local Sardinians to celebrate Italy's victory over Austria.

The local newspaper, L'Unione Sarda, published a front-page editorial today saying the fear of the soccer hooligans was becoming a reality. "They have killed the dream of a party," it said. "An explosive mixture of alcohol and violence has delivered the first blow to the public image that English soccer is struggling to rebuild."

English club teams have been barred from European cup competitions since Liverpool and Juventus fans rioted during a 1985 match in Brussels. Thirty-nine people were killed.