Basket options have long been an important structured product. Although basket options have been extensively studied in the literature, there are few published papers that deal with the pricing of basket options with stochastic interest rates. This study presents two novel basket option pricing models that permit the interest rates to be random. The paper presents a powerful calculation technique for the problem when underlying stock returns are continuous. Finally, we use a regular grid method to the calculation of the formula of two-asset basket option when underlying stock returns are continuous and a mixture of both the regular grid method and a Monte Carlo method to the one when underlying stock returns are discontinuous, and sensitivity analyses are presented.