This paper describes the comprehensive mathematical modeling, simulation and finally validation the developed dynamic equations of a pressurizable liquid piston Stirling engine. The proposed system comprises of the main following components: solar fresnel lens, hot, cold and tuning liquid columns, regenerator, solid pressure intensifier, liquid power piston and output water column. The mathematical modeling of the proposed system is divided into distinct parts, including dynamic of working gas pressure, hot, cold and tuning liquid columns and dynamic of the output part of the system. The obtained dynamic differential equations are rewritten to nine first order differential equations and solved employing 4th order Runge-Kutta numerical method. The pumping head of 1.5 m, the hot and cold side temperature of 100 degrees C and 20 degrees C, respectively and zero dead volumes are considered. It is obtained that the working gas pressure has the oscillatory behavior between two upper and lower points, frequently. According to the oscillatory dynamic of working gas pressure, when the working gas pressure is high enough, it can push the liquid power piston to overcome the static pressure of the output column of the pump and finally the water pumping occurs. (C) 2018 Elsevier Ltd. All rights reserved.