Dislocation mediated plasticity in the alpha phase of the energetic molecular crystal cyclotrimethylene trinitramine (RDX) was investigated using a combination of atomistic simulations and the Peierls-Nabarro (PN) model. A detailed investigation of core structures and dislocation Peierls stress was conducted using athermal atomistic simulations at atmospheric pressure to determine the active slip systems. Generalized stacking fault energy surfaces calculated using atomistic simulations were used in the PN model to also estimate the critical shear stress for dislocation motion. The primary slip plane is found to be (010) in agreement with experimental observations, with the (010)[100] slip systems having the lowest Peierls stress. In addition, atomistic simulations predict the (021)[0 (1) over bar2], (021)[100], (011)[100], (001)[100], and (001)[010] slip systems to have Peierls stress values small enough to allow plastic activity. However, there are less than five independent slip systems in this material in all situations. The ranking of slip systems based on the Peierls stress values is provided, and implications are discussed in relation to experimental data from nanoindentation and shock-induced plastic deformation.