Studying the movements of short interest rates is a very important research field. Almost all banks and investment institutes borrow or lend money with floating interest rates. Thus, this study is essential to measure the risk and hedge it or to speculate a possible gain in the future. In this work we will focus on researching the short interest rates movements using Vasicek model and review some other models. Simulations for the interest rates and market instruments are presented using the Vasicek model in R.