In this paper, we address a physics based closed form model for the energy band gap (E-g) and the transport electron effective mass in relaxed and strained [100] and [110] oriented rectangular Silicon Nanowire (SiNW). Our proposed analytical model along [100] and [110] directions are based on the k.p formalism of the conduction band energy dispersion relation through an appropriate rotation of the Hamiltonian of the electrons in the bulk crystal along [001] direction followed by the inclusion of a 4 x 4 Luttinger Hamiltonian for the description of the valance band structure. Using this, we demonstrate the variation in Eg and the transport electron effective mass as function of the cross-sectional dimensions in a relaxed [100] and [110] oriented SiNW. The behaviour of these two parameters in [100] oriented SiNW has further been studied with the inclusion of a uniaxial strain along the transport direction and a biaxial strain, which is assumed to be decomposed from a hydrostatic deformation along [001] with the former one. In addition, the energy band gap and the effective mass of a strained [110] oriented SiNW has also been formulated. Using this, we compare our analytical model with that of the extracted data using the nearest neighbour empirical tight binding sp(3)d(5)s* method based simulations and has been found to agree well over a wide range of device dimensions and applied strain. (C) 2012 Elsevier Ltd. All rights reserved.