In this study, anaerobic digestion tests for municipal solid wastes were performed in order to estimate their methane production rates. To simulate methane production rate, the first derivatives of the sigmoidal equations were calculated. The sigmoidal equations used were Gompertz and Logistic equations. Also, diauxic growth was employed to simulate methane production rate from municipal solid wastes. The equations were fitted to simulate methane production rate by nonlinear regression with a Marquardt-Levenberg algorithm. This is a statistical analysing methodology to minimize the sum of the squares of the differences between the predicted and measured values. Data fittings obtained by using the equations were compared statistically by using the RMSE (Root mean square error) and AIC (Akaike's information criterion). The equations derived from sigmoidal equations successfully described methane production rate for municipal solid wastes. RMSE and AIC were decreased significantly for the equations considering diauxic growth, compared to the equations without diauxic growth. These results showed that the equations derived from sigmoidal equations with diauxic growth can be a useful tool to simulate methane production rate for municipal solid wastes.