Laser-induced Breakdown Spectroscopy (LIBS) is actively under development for future use on surface probes to Mars. The analytical method can be deployed for in-situ and/or stand-off analysis with the latter embodiment providing the greatest advantages compared to previous and current elemental analysis methods used for planetary surface analysis. For this application, LIBS must be thoroughly investigated in terms of analytical capabilities and flight-rated instruments must be developed. Because of the low pressure of the predominantly CO2 atmosphere on Mars, studies are needed to understand analytical requirements and to determine performance under these conditions. Stand-off analysis demands the most stringent requirements on instrumentation. Therefore, it must be determined if the high performance components that are normally used in a typical LIBS laboratory setup, which are generally not optimized for small size and weight, are essential to obtain the maximum scientific return from a mission. A key component of a LIBS apparatus is the detection system consisting of a spectrograph and a detector. Here we present an evaluation of one design of a compact spectrograph (Ocean Optics HR2000) for in-situ and stand-off LIBS analyses of geological samples under Mars atmospheric conditions.