Common analytical models to predict the unidirectional compressive strength of fibre reinforced polymers are analysed in terms of their accuracy. Several tests were performed to determine parameters for the models and the compressive strength of carbon fibre reinforced polymer (CFRP) and glass fibre reinforced polymer (GFRP). The analytical models are validated for composites with glass and carbon fibres by using the same epoxy matrix system in order to examine whether different fibre types are taken into account. The variation in fibre diameter is smaller for CFRP. The experimental results show that CFRP has about 50% higher compressive strength than GFRP. The models exhibit significantly different results. In general, the analytical models are more precise for CFRP. Only one fibre kinking model’s prediction is in good agreement with the experimental results. This is in contrast to previous findings, where a combined modes model achieves the best prediction accuracy. However, in the original form, the combined modes model is not able to predict the compressive strength for GFRP and was adapted to address this issue. The fibre volume fraction is found to determine the dominating failure mechanisms under compression and thus has a high influence on the prediction accuracy of the various models.