As SOI technology becomes very attractive for ULSI CMOS, a dedicated and accurate SOI model has to be developed in order to take into account all specific electrical effects related to the SOI structure. The LETISOI model has been developed for partially depleted SOI devices; current and charge equations are built on a physical basis. In addition to the classical MOS conduction, FB effects, self-heating and bipolar transistor action have to be accurately modeled. The transient behavior, very different from the static one, has to be analyzed and kept in mind by designers to take full benefit of SOI devices in circuits, while avoiding any design issue due to SOI. Both FB and body-contacted devices can be described with this model. This paper describes how the model is built with an emphasis on the specific SOI needs and the related strategy for parameter extraction. Typical simulation results are also presented, outlining the capability of the model to simulate SOI specific dynamic behavior like bipolar activation and history effects.