In future high-speed communication, it is anticipated that cases dealing with fixed-length data will increase. Therefore, a traffic analysis for constant-service-time models is needed. In this paper, a multiserver queuing model M / D / s / N for finite capacity in the system and constant service time is treated. By discrete approximation, its steady-state analysis is attempted. In this analysis, the state at each discrete time step chosen at a constant interval of about 1/10 of the service time is defined by the number of calls in the system and the residual service time for each server. By considering the state transition probability within this time, linear simultaneous equations in the state variables for the previous and next discrete time steps are solved to derive the steady-state probability. In the calculation of the state transition probability, we assume that the departures and arrivals of calls are approximately uniformly distributed. The approximate numerical results are compared with high-precision simulation results as well as with those obtained by applying an existing approximation on M / G / s / N to a constant service time. It is shown that the calculated steady-state probability generally has good accuracy.