We report on efforts to perform theoretical modeling of the emission spectrum measured from a basalt sample. We compare our calculations with measurements that were made to provide standards for the ChemCam instrument on the Mars Science Laboratory. We find that to obtain good agreement between modeling and the measurement, it is necessary to determine atomic and ionic level populations via a multi-element approach in which the free electron density that is created influences all the species within the plasma. Calculations that consider each element separately are found to be in poorer agreement with the measured spectrum, indicating that the ‘matrix effect’ term often used to describe the influence of other species on the emission spectrum from a given element is due to the influence of the global electron density of the plasma. We explore the emission features in both the visible and near-infrared wavelength ranges, and also examine radiation transport effects for some of the most intense features found in the basalt spectrum. Finally, we also provide comparisons of the ChemCam measurement with new high-resolution spectral measurements.