Hybrid plasma simulations, consisting of kinetic ions treated using standard Particle- In-Cell (PIC) techniques and an inertialess charge-neutralizing electron fluid, have been used to investigate the properties of collisionless shocks for a number of years. They agree well with sparse data obtained by flying through Earth’s bow shock and have been used to model high energy explosions in the ionosphere. In this doctoral dissertation hybrid plasma simulation is used on much smaller scales to model collisionless shocks in a controlled laboratory setting. Initially a two-dimensional hybrid code from Los Alamos National Laboratory was used to find the best experimental parameters for shock formation, and interpret experimental data. It was demonstrated using the hybrid code that the experimental parameters needed to generate a shock in the laboratory are relaxed compared to previous work that was done[1]. It was also shown that stronger shocks can be generated when running into a density gradient. Laboratory experiments at the University of California at Los Angeles using the high energy kJ-class Nd:Glass 1053 nm Raptor laser, and later the low energy yet high repetition rate 25 J Nd:Glass 1053 nm Peening laser have been performed in the Large Plasma Device (LAPD), which have provided some much needed data to benchmark the hybrid simulation method. The LAPD provides a repeatable, quiescent, ambient magnetized plasma to surround the exploding laser produced plasma that is ablated from a High Density Polyethylene (HDPE) target. The plasma density peaks in the machine at n_i ∼ O(10^13 cm^−3), which is sufficiently dense to strongly couple energy and momentum from a laser ablated carbon plasma ejected from the HDPE target into the magnetized ambient plasma. It has been demonstrated that a sub-critical shock is formed in the LAPD using the high energy Raptor laser[2], though the data from this experiment is scant. Hybrid simulation was used as an analysis tool for the shock experiments, but there remained the lingering question as to whether the assumptions made in the model sufficiently capture the relevant ion time scale physics and reproduce the magnetic field structure appropriately. A three-dimensional massively parallel hybrid code package was developed, called fHybrid3D, which was used to reexamine the 2013 data with more realistic laser ablation geometry. The data obtained in the 2015 Peening campaign proved to be useful, even though it did not generate a shock, in that it provided some volumetric data to compare to the 3D hybrid simulation. In addition to the larger magnetic field data sets, an emissive probe designed at UCLA[3] was fielded that could measure plasma potential. This is an important measurement, as previously only magnetic fields were measured on the ablation blow-off axis during the high energy laser experiments. This allows the laboratory experiment to directly validate the use of a simple isotropic electron pressure model close to the target. Though through scaling arguments the Larmor fields are strongest and provide the bulk of the ambient ion acceleration, correctly modeling the radial electric fields in the realm of sub-critical shocks is important for getting the coupling right as at lower Mach numbers. The data collected that is compared to simulation output that was converted to electrostatic potential φ suggests that the electron pressure model is sufficient for modeling perpendicular shocks in the laboratory.