Signal processing and multimedia applications are commonly modeled using Static/Cyclo-Static Dataflow (SDF/CSDF) models. SDF/CSDF explicitly specifies how much data is produced and consumed per firing during computation. This results in strong compile-time analyzability of many useful execution properties such as deadlock absence, channel boundedness, and throughput. However, SDF/CSDF is limited in its ability to capture how data is accessed in time. Hence, using these models often leads to implementations that are sub-optimal (i.e., use more resources than necessary) or even incorrect (i.e., use insufficient resources). In this work, we advance a new model called Static Dataflow with Access Patterns (SDF-AP) that captures the timing of data accesses (for both production and consumption). This paper formalizes the semantics of SDF-AP, defines key properties governing model execution, and discusses algorithms to check these properties under correctness and resource constraints. Results are presented to evaluate these analysis algorithms on practical applications modeled by SDF-AP.