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The paper presents a Computational Fluid Dynamics (CFD) model of the cold alpha-type Stirling engine. The developed mathematical model comprises of Unsteady Reynolds Averaged Navier-Stokes (URANS) set of equations, i.e. continuity, momentum and energy equations. Moreover, the developed mathematical model comprises a non-equilibrium description of the regenerator, by the introduction of the energy conservation equation for the regenerator matrix. It was implemented in the framework of commercial CFD software ANSYS Fluent. The work presents an in-depth analysis of the influence of the numerical mesh and applied turbulence model on the obtained results. The model was used to analyse the influence of the regenerator on the performance of the cold Stirling engine at different operating conditions. It appeared that on an average application of the regenerator increased the engine specific work by 10 J/kg and this increase is significantly higher at a high rotational speed of the engine. At the same time, the engine efficiency averagely was increased by 10 percent points and again this increase was significantly higher at higher rotational speeds of the engine. Especially, the influence of the heat source and sink temperatures on the engine operation were analysed. It appears that the lower are temperatures of a heat source and sink the more pronounced is the presence of the regenerator in the engine. Finally, the influence of the elementary parameters: particle diameter and porosity of the solid matrix which constitute the regenerator filling was investigated. It was shown that for the analysed engine the optimal value of the regenerator packing porosity equals about 0.72 it results in the specific area of the regenerator equal around 1675 m2/m3. Obtained results can be used to analyse the possibility of application of Stirling engines to recover low-temperature exergy of regasified Liquified Natural Gas (LNG), which for small regasification units can be alternative for commonly utilised Ambient Air Vaporizers (AAV) and it aside for regasification of LNG it could produce electric energy. [ABSTRACT FROM AUTHOR]