A first step in a comparative study is made between simulations and ISEE satellite observations of quasi-parallel interplanetary shocks. In this study we compare the magnetic field structures for three shock cases. A hybrid code is used in the simulation which is found to reproduce reasonably well the overall structures of low Mach number quasi-parallel shocks in the laminar regime. The frequency, wavelength, and wave amplitude deduced from simulations are in reasonable agreement with observations.