A machining simulation apparatus (1) includes a model storage (4) for storing information about machining models (11) that define mechanical elements, such as spindle heads and tables, jig models (12) that define jigs, such as chucks and holders, material models (13) that defines the shapes of workpieces, and tool models (14) that defines the shapes of tools for machining the workpieces. Each tool model comprises a machining tool model (14A) and an interference check tool model (14B). A material model is machined with the machining tool model (14A) according to an axis movement command for cutting feed so as to update the shape of the material model. Subsequently, interference of the interference check tool model with the material model, jig models, and machine models are checked for according to an axis movement command for rapid traverse.