Short-term interest rate models within one-year financing maturity are considered. In this thesis, we mainly study two short-term interest rate models, the Cox-Ingersoll-Ross model (CIR model) and the Vasicek model. The CIR model is evaluated by numerical simulations based on applying the Euler approximation method and an exact algorithm. By using an ordinary least squares method we can find an initial start value for implementation of a numerical estimate of parameters that maximize the likelihood. Similarly applying those methods to the Vaˇs ́ıˇcek model, we compare the two models with empirical data based on three-month money market rates.