•A numerical model for designing a free piston Stirling engine is proposed.•A prototype engine is designed and analyzed using proposed model.•The transient behaviors and performance of prototype engine are simulated.•Effects of loading and charged pressure on the performance are studied. A free piston Stirling engine is a complex system that its transient behaviors of thermal properties and dynamic characteristics are coupled with each other. In order to assess the performance of the engine, the prediction of the aforementioned properties becomes unavoidable. In this study, a modified non-ideal adiabatic model and a dynamic model were solved simultaneously for determining the thermal properties of the working fluid and the dynamic behaviors of the displacer and piston. The energy equations of the working fluid in each working space were solved. The variations in the temperature, mass, and pressure of the working fluid in each working space in each time step were predicted. The displacements of the displacer and piston were also solved. The proposed model was used for predicting the phase angle, amplitude, frequency, power, and efficiency of the engine. A prototype engine was also designed on the basis of the proposed model. The performance of the prototype engine under different loading and charged pressure was studied. The results indicated that optimum charged pressure and loading values exist for achieving the maximum power output and efficiency. For the prototype engine, the maximum power reached 595 W at an operating frequency of 66.26 Hz and charged pressure of 50 bar.