Scenario-based specifications such as message sequence charts (MSCs) offer an intuitive and visual way of describing design requirements. As one powerful formalism, Petri nets can model concurrency constraints in a natural way, and are often used in modelling system specifications and designs. Since there are gaps between MSC models and Petri net models, keeping consistency between these two kinds of models is important for the success of software development. In this paper, we use Petri nets to model concurrent systems, and consider the problem of checking Petri nets for scenario-based specifications expressed by message sequence charts. We develop the algorithms to solve the following two verification problems: the existential consistency checking problem, which means that a scenario described by a given MSC must happen during a Petri net runs, or any forbidden scenario described by a given MSC never happens during a Petri net run; and the mandatory consistency checking problem, which means that if a reference scenario described by the given MSCs occurs during a Petri net run, it must adhere to a scenario described by the other given MSC.