A three-dimensional (3D) transient finite element formulation for modeling laser processing is presented, with the capability to simulate both additive manufacturing and laser ablation physics. State variables are introduced to model the phase change phenomenon and to track the phase and phase history throughout the simulation. Temperature dependent material properties are used to capture the nonlinearity of a typical phase change problem. A level set approach is introduced in the subtractive manufacturing simulation, in order to effectively track the rapidly receding surface due to material vaporization and to update the incoming energy distribution for the pulsed laser source on the new geometry. The 3D finite element simulation is implemented in a parallel multi-physics finite element solver, enabling high-performance computation. Simulation results, for both additive and subtractive manufacturing, are acquired, where the size of melt pool and ablation region (width and depth) are predicted quantitatively.