Abstract: This paper model and forecast monthly exchange rates of US Dollar to Sri Lankan Rupee using Constant Elasticity of Variance (CEV) Model. In this study, five models are formulated considering five elasticity factors 0,1⁄2,1,3⁄2and 2. Monthly exchange rates from January, 1995 to December, 2016 were obtained from the official website of Central Bank of Sri Lanka. Among this data, 254 observations were used to estimate the parameters and other 10 observations were used to test the validity of the models. To estimate the parameters, maximum likelihood estimation method is used and the exchange rates are generated using Euler- Maruyama method. The Monte Carlo technique is used for simulation and the accuracy of the forecasts is compared with Root Mean Squared Error (RMSE) and Mean Absolute Percentage Error (MAPE). The model which has the minimum RMSE and MAPE is chosen as the best model to predict the monthly exchange rate of LKR/USD.