Park came to the Winston Cup Series as the driver for the No. 14 team of Dale Earnhardt Inc. (DEI) in 1997. He attempted eight races in this car, qualifying for four of them. He also ran a race in the No. 40 car at Martinsville Speedway for Felix Sabates. In the 1998 season, Park switched to the No. 1 Chevrolet for DEI and drove the first two races, but he failed to qualify at the third race of the year at Las Vegas. During practice for the fourth event of the year at Atlanta Motor Speedway, Park suffered a tire failure and had three hard hits before his car came to rest. He sustained a broken leg, broken collarbone, broken shoulder blade, and two chipped front teeth. Park returned later in the year at Indianapolis Motor Speedway and ran the rest of the year. He posted a best finish of 11th at Michigan and Dover.