We evaluate the capacity of direct sequence code-division multiple access (DS-CDMA) systems supporting multiclass on/off traffic in a multiple cell environment. For this purpose, given the requirements of bit energy-to-interference power spectral density ratios and outage probabilities, we obtain a set of all admissible points satisfying those requirements. Whether a point, denoting the number of calls for each class, is admissible or not is determined by numerically solving the nonlinear equations representing the service requirements.