Modular origami is a type of origami where multiple pieces of paper are folded into modules, and these modules are then interlocked with each other forming an assembly. When the flexibility of the modular origami is considered, the motion trajectory can be changed and the motion can even be locked. Many numerical approaches have been proposed to simulate the motion of origami. Here we focus on the finite particle method (FPM) and derive a formulation for modular origami models. Based on the FPM, we simulate motion of modular origami. Both 2D and 3D examples are given to verify the proposed formulation. This work paves the way for achieving the controllable motion paths of the flexible modular origami structures.