We propose a static analysis technique that computes upper bounds of virtual machine usages in a concurrent language with explicit acquire and release operations of virtual machines. In our language it is possible to delegate other (ad-hoc or third party) concurrent code to release virtual machines (by passing them as arguments of invo-cations). Our technique is modular and consists of (i) a type system associating programs with behavioural types that records relevant information for resource usage (creations, releases, and concurrent operations), (ii) a translation function that takes behavioural types and return cost equations, and (iii) an automatic off-the-shelf solver for the cost equations. A soundness proof of the type system establishes the correctness of our technique with respect to the cost equations. We have experimentally evaluated our technique using a cost analysis solver and we report some results. The experiments show that our analysis allows us to derive bounds for programs that are better than other techniques, such as those based on amortized analysis.