The process of laser beam welding is modeled using the mess-free Lagrangian Smoothed Particle Hydrodynamics (SPH) method. The Weakly-Compressible SPH (WCSPH) model for laser beam welding in [1] is compared with an Incompressible SPH (ISPH) model. While in WCSPH small density changes are allowed and the pressure is related to the density by an artificial equation of state, in ISPH the density is constant and the pressure is calculated by solving a pressure Poisson equation that enforces incompressibility by projecting an intermediate velocity field onto a divergence-free space. The presented models based on the WCSPH and ISPH method consider significant physical effects during laser beam welding like heat conduction, temperature-dependent surface tension, wetting, the phase transitions melting and solidification, and an evaporation-induced recoil pressure. The laser-material interaction is modeled by coupling the SPH method with a ray tracer that calculates the locally absorbed intensity on the material surface by means of geometrical optics. The models are applied to deep penetration laser beam welding. For the first time using the SPH method, the effect of an oscillating laser power on the capillary depth is investigated. By validating the numerical results with experimental observations, the accuracy of the WCSPH and the ISPH model is compared. The results show that both methods are able to represent the main characteristics of the laser beam welding processes such as the melt pool size and the formation of a vapor-filled capillary. Compared to WCSPH, the ISPH model allows larger time step sizes and thus can be computationally more efficient for the simulation of laser beam welding processes.