In the last two decades there has been an increasing interest in the field of haptics science. Real-time simulation of haptic interaction with non-rigid deformable object/tissue is computationally demanding. The computational bottleneck in finite- element (FE) modeling of deformable objects is in solving a large but sparse linear system of equations at each time step of the simulation. Depending on the mechanical properties of the object, high-fidelity stable haptic simulations require an update rate in the order of 100 − 1000 Hz. Direct software-based implementations that use conventional computers are fairly limited in the size of the model that they can process at such high rates. In this thesis, a new hardware-based parallel implementation of the iterative Conjugate Gradient (CG) algorithm for solving linear systems of equations is pro- posed. Sparse matrix-vector multiplication (SpMxV) is the main computational kernel in iterative solution methods such as the CG algorithm. Modern micro- processors exhibit poor performance in executing memory-bound tasks such as SpMxV. In the proposed hardware architecture, a novel organization of on-chip memory resources enables concurrent utilization of a large number of fixed-point computing units on a FPGA device for performing the calculations. The result is a powerful parallel computing platform that can iteratively solve the system of equations arising from the FE models of object deformation within the timing constraint of real-time haptics applications. Numerical accuracy of the fixed-point implementation, the hardware architecture design, and issues pertaining to the degree of parallelism and scalability of the solution are discussed in details. The proposed computing platform in this thesis is successfully employed in a set of haptic interaction experiments using static and dynamic linear FE-based models. / Master of Applied Science (MASc)