The specification of money demand function is one of the most important and disputable subjects in economics. With regard to its importance, many of economists have represented several theorizes about money demand. The Sidrauski monetary model is an interesting theory of money demand. Sidrauski extended Ramsey model with regard real balance of money which in the Sidrauski model the utility function involves both consumption and money. Application of Sidrauski model can help to extend macroeconomics with micro foundations in Iran and prepares new scopes for researchers. The main aim of this paper is to estimate the Sidrauski monetary model for Iranian economy over the period of 1979 -2011. For this purpose, the Engle – Granger, ARDL and Johansen- Juselius approaches have been used for estimation of long run relationship of money demand. The empirical results of econometric estimation of co-integration vector indicated a long run relationship between per capita money demand, per capita consumption, and inflation rate, rate of interest, exchange rate, per capita income, and stock exchange price index. Our results showed that per capita consumption and per capita income have positive and significant effect on per capita money demand. Whereas inflation rate, rate of interest, exchange rate and stock exchange price index have negative and significant effect on per capita money demand.