<p>The aim of this paper is to study the numerical solutions of linear elliptic and parabolic stochastic partial differential equations driven by fractional Brownian motion. We first construct approximations for fractional Brownian noise and fractional white noise, respectively. Using these approximations, we establish numerical solutions, which are shown to converge to the exact solution as the mesh size decreases. Then, we provide discrete formulations of the numerical solutions using difference and finite element approximations, and analyze their errors. Finally, we illustrate the convergence of these methods by a numerical example.</p>