Stateflow models are complex software models, often used as part of safety-critical software solutions designed with Matlab Simulink. They incorporate design principles that are typically very hard to verify formally. In particular, the standard exhaustive formal verification techniques are unlikely to scale well for the complex designs that are developed in industry. Furthermore, the Stateflow language lacks a formal semantics, which additionally hinders the formal analysis. To address these challenges, we lay here the foundations of a scalable technique for provably correct formal analysis of Stateflow models, with respect to invariant properties, based on bounded model checking (BMC) over symbolic executions. The crux of our technique is: i) a representation of the state space of Stateflow models as a symbolic transition system (STS) over the symbolic configurations of the model, as the basis for BMC, and ii) application of incremental BMC, to generate verification results after each unrolling of the next-state relation of the transition system. To this end, we develop a symbolic structural operational semantics (SSOS) for Stateflow, starting from an existing structural operational semantics (SOS), and show the preservation of invariant properties between the two. Next, we define bounded invariant checking for STS over symbolic configurations as a satisfiability problem. We develop an automated procedure for generating the initial and next-state predicates of the STS, and propose an encoding scheme of the bounded invariant checking problem as a set of constraints, ready for automated analysis with standard, off-the-shelf satisfiability solvers. Finally, we present preliminary results from an experimental comparison of our technique against the Simulink Design Verifier, the proprietary built-in tool of the Simulink environment.