We study the sensitivity of fixed target neutrino experiments (LSND, T2K, CENNS, and COHERENT) and proton beam dumps (MiniBooNE off-target, and SHiP) to sub-GeV dark matter. In order to reproduce the observed thermal relic abundance, these states are coupled to the Standard Model via new, low mass mediators in the form of a kinetically mixed U(1)0 vector mediator or a vector mediator gauging baryon number. We present a model for the production of low mass dark matter from proton-nucleon collisions in fixed targets. Sensitivity projections are made using signals from elastic electron- and nucleon-dark matter scattering, as well as coherent nuclear-dark matter scattering and dark matter induced inelastic π 0 production. A fixed target Monte Carlo code has been developed for this analysis, and documentation is included. We find that analyses using current and future proton fixed target experiments are capable of placing new limits on the hidden sector dark matter parameter space for dark matter masses of up to 500\,MeV and mediator masses as large as a few GeV. / Graduate