The use of computer simulations in the teaching of introductory statistics can help undergraduate students understand difficult or abstract statistics concepts. The free software environment R is a good candidate for computer simulations since it allows users to add additional functionality by defining new functions. In this paper, we illustrate how computer simulations with R are used in statistics classrooms and student homework assignments by examples. These examples include sampling distributions and the central limit theorem, the t-distributions, confidence intervals, hypothesis testing, regression analysis and nonparametric tests.