The present study has been focused on the acid and base Transesterification of animal fats (dairy cow and beef) to produce biodiesel by varying process parameters such as catalyst amount, catalyst nature, reaction time and temperature. The maximum biodiesel yield after acid catalysis was 94.1±2.43 and 98.4±2.3 percent for dairy cow and beef tallow, respectively. The quantity of biodiesel obtained after base catalysis was comparatively lower than obtained in case of the acid catalysis. The optimum conditions for biodiesel production using acid catalysis were: 2.5 g of conc. H2SO4, 24 h of reaction time and 50oC for dairy cow fat and 2.5 g of conc. H2SO4, 6 h of reaction time and 60oC for beef fat. The amount of biodiesel obtained from beef tallow in the present study was much higher than earlier reported yields. The evaluation of Transesterification process was followed by gas chromatographic analysis of tallow fatty acid esters (biodiesel) at optimal conditions. The fuel properties of biodiesel thus obtained accomplished the requirements of both the American and European standards for biodiesel.