One popular approach to overcome the expected congestions due to the spectacular development of various multimedia applications consists in installing transparent caches at strategically chosen places inside telecommunication networks. The problem of locating caches is a difficult optimization problem, closely related to the p-median problem. In the case where the network is a tree, some cache location problems have already been investigated. In this paper, we propose to refine these models by taking into account a dynamic effect due to cache replacement policies. In our model, only the most popular contents are stored in the caches. The hierarchical effect of several successive caches is also captured by the model. A Mixed Integer Programming model and a Dynamic Programming algorithm are proposed and compared on a preliminary set of numerical experiments.