This paper investigates the stability of the money demand function for Sweden between 1993Q1 and 2016Q4. The demand for money is expressed as a function of a scale variable and an opportunity cost variable. The money measure used is M3 while GDP from the expenditure side is used as a proxy for the scale variable and the interest rate on the 90day Swedish government bond is used as the opportunity cost variable. After a theoretical discussion about the importance, and implications, of a stable money demand function is provided, the paper empirically test the stability of the function. Johansen cointegration technique is employed and one cointegration equation between the variables is found. An error correction model is estimated and subject to CUSUM and CUSUMQ stability tests. The results indicate a stable money demand function for the given variables.