Monte Carlo simulation of clinical treatment plans require, in general, a coordinate transformation to describe the incident radiation field orientation on a patient phantom coordinate system. The International Electrotechnical Commission (IEC) has defined an accelerator coordinate system along with positive directions for gantry, couch and collimator rotations. In order to describe the incident beam's orientation with respect to the patient's coordinate system, DOSXYZnrc simulations often require transformation of the accelerator's gantry, couch and collimator angles to describe the incident beam. Similarly, versions of the voxelized Monte Carlo code (VMC(++)) require non-trivial transformation of the accelerator's gantry, couch and collimator angles to standard Euler angles α, β, γ, to describe an incident phase space source orientation with respect to the patient's coordinate system. The transformations, required by each of these Monte Carlo codes to transport phase spaces through a phantom, have been derived with a rotation operator approach. The transformations have been tested and verified against the Eclipse treatment planning system.