The simultaneous productions of mechanical work and low-grade heat by a Stirling engine cogeneration powered by crude glycerol are studied analytically. The study focuses on searching the appropriate values of engine physical parameters to minimize the specific fuel consumption to optimize the work production regardless of the low-grade heat production. The modeling considers the equation of combustion , finite heat transfer between the sources and the working gas, non-perfect regenerator, non-isothermal transformations and non-sinusoidal volume variations during the crankshaft rotation. The optimum operating temperature of the engine hot source and the optimum piston-displacer angular phase shift are determined for alpha, beta and gamma Stirling engines according to the engines swept volume ratio. Results show that the optimum configuration changes considerably with the value of the coefficient of heat transfer. The minimum specific glycerol consumption is 1024 g gly ./kWh and is obtained with alpha type engine. Best performance for beta type is quasi-similar but in this last case, the indicated work production is higher than for alpha engine.