In this paper, we present a new analytical physics-based drain current model for single source/drain and fully overlapped and partially overlapped lightly-doped-drain (LDD) fully-depleted (FD) SOI MOSFETs. The model was developed by starting from the two-dimensional (2-D) Poisson equation, and including the effects of series resistances and velocity saturation. In particular, the phenomenon of front surface accumulation and depletion in the LDD region is included in the model to describe saturation I-V characteristics. The device is partitioned into the source, intrinsic channel, subdiffusion, and overlapped and non-overlapped LDD regions. The device parameters, such as local threshold voltage and doping concentration, are continuous along the channel. The model can describe the I-V characteristics and can be used to calculate the lateral electric fields in the channel region and in the LDD region for the device operated in both the linear and saturation regions. It also considers the effects of impact ionization and self-heating in SOI devices. The accuracy of the presented model has been Verified with the experimental data of single source/drain and LDD SOI devices.