This study is aimed at development of a numerical model for a beta-type Stirling engine with rhombic-drive mechanism. By taking into account the non-isothermal effects, the effectiveness of the regenerative channel, and the thermal resistance of the heating head, the energy equations for the control volumes in the expansion chamber, the compression chamber, and the regenerative channel can be derived and solved. Meanwhile, a fully developed flow velocity profile in the regenerative channel, in terms of the reciprocating velocity of the displacer and the instantaneous pressure difference between the expansion and the compression chambers, is derived for calculation of the mass flow rate through the regenerative channel. In this manner, the internal irreversibility caused by pressure difference in the two chambers and the viscous shear effects due to the motion of the reciprocating displacer on the fluid flow in the regenerative channel gap are included. Periodic variation of pressures, volumes, temperatures, masses, and heat transfers in the expansion and the compression chambers are predicted. A parametric study of the dependence of the power output and thermal efficiency on the geometrical and physical parameters, involving regenerative gap, distance between two gears, offset distance from the crank to the center of gear, and the heat source temperature, has been performed. (C) 2010 Elsevier Ltd. All rights reserved.