As mobile communication systems have been widespread and the needs for new service grows, IMT-2000 systems have largely been researched and developed for standardization. Among them, Wideband CDMA (WCDMA) solution is standardized in the 3rd Generation Partnership Project. In WCDMA system, voice and high data rate services are supported through dedicated traffic channels, however other packet based services with short duration are provided by using common channels. Data users are allowed to transmit a short message based on a contention manner via the reverse common channels. The basic Common Packet Channel (CPCH) mechanism has been proposed and adopted for accessing common channels. It consists of three phases: Random Access Phase, Collision Resolution Phase, and Data Transmission Phase. To enhance the resource usage efficiency, the CPCH mechanisms with channel assignment or status monitoring have been proposed. They can improve the performance. however increase the system complexity. Up to now, performances of the CPCH mechanisms have been discussed and studied based on computer simulations. Numerical results have been obtained by using S-G analysis, but they are different from simulation results. In this paper, we analyze the CPCH mechanisms by using the Equilibrium Point Analysis (EPA). And we compare computer simulation results with analytical results.