Using density functional theory combined with an evolutionary algorithm for crystal structure prediction, we study the elastic and electronic properties of various multi-principal element alloys that are based on CoCrFeNi. In total, nine quinary and one senary CoCrFeNiX (X ¼ Ti, V, Mn, MnV, Cu, Zr, Nb, Mo, Al, Al 2 ) alloys are studied along with the base CoCrFeNi alloy. The aim of the current study is twofold. First, we test and confirm the ability of the presented methodology to predict the crystal structure of the multi-principal element alloys based on Co, Cr, Fe, and Ni elements. Second, we calculate and compare the elastic properties of the CoCrFeNiX alloys, as well as their electronic properties, in an attempt to establish possible correlations between them. Taking CoCrFeNi as the reference alloy, our first-principles calculations of various elastic moduli (bulk, Young, and shear moduli) show that only the bulk moduli of the alloys with Cu, Mo, or Nb (in this order) are expected to be larger. Furthermore, our comparative analysis of the CoCrFeNiX alloys containing partially filled 3d and 4d elements shows that the filling of the d-shell causes a general increase in all the elastic moduli. The only exception is the decreasing behavior of the bulk modulus in the case of alloys with partially filled 3d elements.