Results of theoretical simulations of the dynamic solar thermal desalination unit with a fluid piston are presented in this paper. A laboratory prototype of a dynamic thermal water distillation unit was developed at Durham University and it was built around an engine with fluid pistons. In the calculation scheme, the internal circuit of the desalination unit was split into several control volumes including the evaporator, the condenser and the cylinder. The lumped parameter mathematical model was derived based on the differential energy and mass conservation equations written for each of the control volumes and it takes into account heat and mass transfer processes taking place during water evaporation and condensation under cyclic variation of the pressure and temperature inside the system when the engine is operational. Solution of the set of governing equations produces information on variation of temperatures and pressure inside the system over the thermodynamic cycle and on water desalination capacity of the unit.