Enhanced Porosity Concrete (EPC), also known as pervious concrete is a macroporous material that is finding applications in parking areas and low volume pavements because of its ability to transport a large amount of storm water through its porous material structure. Majority of the current research focuses on the functional performance of this material, with scant research on its mechanical behavior. In this study, a computational procedure is implemented on two-dimensional planar images of EPC to reconstruct three-dimensional material structures. The 3D reconstructed digital image data is used as an input to a finite element program to calculate the effective linear elastic properties of the material when subjected to applied macroscopic strains. EPC consists of three phases - the aggregates, the paste surrounding the aggregates, and the pores. In order to reduce the complications associated with assigning each of these phases different elastic moduli, each aggregate (assumed to be spherical in shape) surrounded by a paste shell, is mapped into an effective particle having a uniform elastic modulus, which is then input into the program to calculate the effective elastic modulus of the composite. The paste thicknesses for different EPC mixtures are obtained from an image analysis procedure. Ultrasonic pulse velocity method is used to experimentally determine the elastic modulus of several EPC mixtures proportioned using different aggregate sizes and blends. The results of the predictions using the computational method, and the experimental values are in good agreement.