With the widespread use of GPUs, it is important to ensure that programmers have a clear understanding of their shared memory consistency model i.e. what values can be read when issued concurrently with writes. While memory consistency has been studied for CPUs, GPUs present very different memory and concurrency systems and have not been well studied. We propose a collection of litmus tests that shed light on interesting visibility and ordering properties. These include classical shared memory consistency model properties, such as coherence and write atomicity, as well as GPU specific properties e.g. memory visibility differences between intra and inter block threads. The results of the litmus tests are determined by feedback from industry experts, the limited documentation available and properties common to all modern multi-core systems. Some of the behaviors remain unresolved. Using the results of the litmus tests, we establish a formal state transition model using intuitive data structures and operations. We implement our model in the Murphi modeling language and verify the initial litmus tests. As a preliminary study, we restrict our model to loads and stores across global and shared memory along with two of the memory fences given in the NVIDIA PTX, thread fence and thread fence block. Finally, we show real world examples of code that make assumptions about the GPU shared memory consistency model that are inconsistent with our proposed model.