Liquid piston Stirling engine, also known as the Fluidyne engine, has been an active subject of research due to its possible integration with renewable energy technologies, like solar energy, providing a sustainable and renewable source for water pumping. Extensive research has been done on the Fluidyne engine, and previous researchers have come up with many designs to improve its efficiency. However, those developed technologies still cannot meet all the demands for practical pumping applications. This is due to the significant losses in the system, resulting in low output power (low output flow rate) and consequently low efficiency. Previous research still lacks a practical and simplified design for its utiliutilisation in agricultural irrigation, replacing the diesel pumps that cause pollution and global warming. Thus, this paper discusses a simplified Fluidyne engine for pumping water in agriculture. The system comprises the following main components: solar Fresnel lens, hot, cold, and tuning liquid columns, regenerator, output water column, and two check valves. Comprehensive mathematical modelling for the whole system is developed, and the dynamic equations that describe each part of the system are derived and simulated using the Runge-Kutta algorithm on MATLAB. The design parameters that have significant effects on the performance of the system are optimised using the dynamic multi-objective genetic algorithm (MOFA) on MATLAB and analysed accordingly for optimum output flow rate.