Abu Dhabi Polytechnic Reactor Simulator (ADPRES) is an open source reactor simulator recently developed at Abu Dhabi Polytechnic. It solves static and time-dependent three-dimensional, multi-group neutron diffusion equation in Cartesian geometries. Fourth order standard Nodal Expansion Method (NEM) is implemented in ADPRES for spatial discretization. The time-dependent diffusion equation is numerically solved by fully-implicit scheme. ADPRES input is straight-forward and designed with minimal keywords. ADPRES also has most features of today's modern reactor simulators. In this paper, ADPRES solutions for several reactor benchmarks were verified. The first part of PWR MOX/UO2 core benchmark was used to verify ADPRES on static reactor problem. For transient reactor problems, LMW three-dimensional and NEACRP 3D PWR transient benchmarks were used. ADPRES solutions were generally accurate and consistent with the solutions from other computer codes. The source codes can be found in the author’s GitHub repository.