This article employed the Hertz contact stress theory and the finite element method to evaluate the maximum contact pressure and the limit stresses of orange fruit under transportation and storage. The elastic properties of orange fruits subjected to axial and axial contact were measured such that elastic limit force, elastic modulus, Poisson’s ratio and bioyield stress were obtained as 18 N, 0.691 MPa, 0.367, 0.009 MPa for axial compression and for radial loading were 15.69 N, 0.645 MPa, 0.123, 0.010 MPa. The Hertz maximum contact pressure was estimated for axial and radial contacts as 0.036 MPa. The estimated limiting yield stress estimated as von Mises stresses for the induced surface stresses of the orange topologies varied from 0.005 MPa–0.03 MPa. Based on the distortion energy theory (DET) the yield strength of orange fruit is recommended as 0.03 MPa while based on the maximum shear stress theory (MSST) is 0.01 MPa for the design of orange transportation and storage system.