The Flexible Periodic Vehicle Routing Problem is the problem of visiting a given set of customers considering a certain periodicity to attend their demands. It is a generalization of the Periodic Vehicle Routing Problem where the fixed schedule constraint is relaxed and the quantity to deliver to each customer at each visit is a decision variable. This flexibility leads to remarkable savings in total costs and this explains the interest in studying the problem and developing effective solution approaches. In this work, an iterative two-phase matheuristic is developed to solve medium and large instances of the problem. Computational tests are made on benchmark instances and on newly generated instances. The results of the matheuristic are compared to the best-known solutions, on small-size instances, and to lower bounds on larger instances. Computational results show that good quality solutions are obtained in a reasonable amount of time.