We consider the problem of reconstructing a 3D mesh of the human body from a single 2D image as a model-in-the-loop optimization problem. Existing approaches often regress the shape, pose, and translation parameters of a parametric statistical model assuming a weak-perspective camera. In contrast, we first estimate 2D pixel-aligned vertices in image space and propose PLIKS (Pseudo-Linear Inverse Kinematic Solver) to regress the model parameters by minimizing a linear least squares problem. PLIKS is a linearized formulation of the parametric SMPL model, which provides an optimal pose and shape solution from an adequate initialization. Our method is based on analytically calculating an initial pose estimate from the network predicted 3D mesh followed by PLIKS to obtain an optimal solution for the given constraints. As our framework makes use of 2D pixel-aligned maps, it is inherently robust to partial occlusion. To demonstrate the performance of the proposed approach, we present quantitative evaluations which confirm that PLIKS achieves more accurate reconstruction with greater than 10% improvement compared to other state-of-the-art methods with respect to the standard 3D human pose and shape benchmarks while also obtaining a reconstruction error improvement of 12.9 mm on the newer AGORA dataset.