In this paper, we address the vehicle routing problem with multiple time windows (VRPMTW), which extends the classic vehicle routing problem to allow customers to be visited only within one or more time windows. We propose a constraint programming (CP) model for the VRPMTW and apply model-strengthening techniques such as fixing variables and adding interval variables to improve the model’s performance. The model’s effectiveness is demonstrated by comparing its performance against an existing mixed-integer programming model. The study also analyzes the differences in solver performance and evaluates the impact of instance characteristics on the solvability of the problem instances. Our study demonstrates the benefits of using a CP model with model-strengthening techniques for solving medium-sized instances of the VRPMTW.