In this paper, we aim to ascribe a meaning to SysML activity diagrams. To this end, we propose a dedicated algebraic-like language, namely activity calculus, and an operational semantics that provides a rigorous and intuitive operational understanding of the behavior captured by the diagram. The semantics covers advanced control flows such as unstructured loops and concurrent control flows. Further more, our approach allows non well-formed control flows, with mixed and nested forks and joins. The probabilistic behaviors as specified in SysML are also considered. This formalization allows us to build a sound framework for the verification and validation of systems design expressed in SysML activity diagrams.