This paper specifies and estimates a short run money demand model for Bangladesh for the period 1974:1-1985:4. After both formal and informal tests of model selection, the Laidler short run real money demand model has been found to be appropriate. Mckinnon, White and Davidson’s (1983) non-nested test of model selection suggests that neither the long-linear nor the linear functional form has any superiority over the other for Bangladesh. Real permanent income and the expected rate of inflation have been found to be the important variables, both theoretically and statistically, in the money demand function. The long run permanent income elasticity of the demand for money has been found to exceed unity. In the case of Bangladesh, the empirical results show that both the demand for narrow and broad money are stable functions.