We present a three-dimensional simulation and calculation of electrical conductivity above the filler percolation threshold for networks containing finite, conductive cylinders as a function of axial orientation (S) and aspect ratio (L/D). At a fixed volume fraction and L/D, the simulations exhibit a critical degree of orientation, S-c, above which the electrical conductivity decreases dramatically. With increasing filler concentration and aspect ratio, this critical orientation shifts to higher degrees of alignment. Additionally, at a fixed volume fraction and L/D, the simulated electrical conductivity displays a maximum at slight uniaxial orientation, which is less pronounced at higher volume fractions and aspect ratios. Our approach can be used as a predictive tool to design the optimal filler concentration and degree of orientation required to maximize electrical conductivity in polymer nanocomposites with conductive cylindrical fillers of finite dimension.