This paper provides an analytical method to evaluate the cell loss probability in ATM (Asyncronous Transfer Mode) networks employing statistical cell multiplexing. A fairly simple design procedure for path/link capacity is also developed. It is demonstrated that the proposed method yields a conservative capacity value over the entire range examined. This was confirmed by comparing the results obtained through the proposed method with computer simulation results. The method yields a link capacity design approach that can effectively handle different bandwidth and types of VPs within the same link. Evaluations show that the method allows 10% to 1400% more traffic than possible with the peak bandwidth allocation scheme in the parameter range we examined; the specified cell loss probability is set at 10-9. As a result, it is shown that the proposed analytical procedure to evaluate the cell loss probability in statistical cell multiplexing, and the path/link capacity design method are effective and practical even though they use fairly simple procedures.