To enable rational design of high entropy alloys (HEAs), we have developed a first principles density functional theory based computational approach to predict the yield strength of single phase HEAs. Specifically, we applied the developed method to calculate the yield strength of some select HEAs with face-centered cubic (fcc) or body-centered lattice (bcc) structure and with varying chemical composition. We have examined our computational approach for four fcc alloy systems, i.e., NiCoFe, CoCrFeNi, CoCrFeCuNi, and RdIrPdPtNiCu, and four bcc alloys systems, i.e., MoNbTaW, MoNbTaV, AlCoCrFeNi, and AlCoCrFeNiZr0.3. For these HEAs with dramatically different chemical composition, our predicted yield strengths are found to agree well with experimental values. Consequently, we have demonstrated that the developed first principles based computational approach is a reliable computational tool for understanding the composition-structure-property relation of HEAs and, particularly, exploring novel HEAs with superior mechanical properties over vast composition space.