This paper introduces the model of
priced timed pushdown systems
as an extension of discrete-timed pushdown systems with a cost model that assigns multidimensional costs to both transitions and stack symbols. For this model, we consider the minimal cost reachability problem: i.e., given a priced timed pushdown system and a target set of configurations, determine the minimal possible cost of any run from the initial to a target configuration. We solve the problem by reducing it to the reachability problem in standard pushdown systems.