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Capacity analysis in wireless communication systems is essential for system design, call admission control and radio resource allocation. Since CDMA is a kind of power-constrained or interference-limited system, its system capacity is not so "hard" as in bandwidth-limited systems, such as TDMA-based systems. In this paper, we analyze the uplink and downlink capacity of multimedia DS-CDMA systems based on constraint models. System capacity is given by feasible condition, which is the sufficient and necessary condition of the existence of feasible solutions to the constraint model. As a byproduct, we also deduct the optimum solution to uplink and downlink transmit power minimization problem, which can be used as references for power control and radio resource allocation multimedia DS-CDMA systems.