This paper addresses the problem of open shop scheduling on two machines with resources constraints. In the context of our study, in order to be executed, a job requires first, for its preparation for a given period of time, a number of resources which cannot exceed a given resource capacity. Then, it goes onto its execution while the resources allocated to it become available again. We seek a schedule that minimizes the makespan. We first prove the NP-hardness of several versions of this problem. Then, we present a well solvable case, lower bounds, and heuristic algorithms along with an experimental study.