Membrane proteins serve a number of important functions for the cell, such as maintaining cell shape and the transport of essential materials into or out of the cell. In a cell membrane, proteins and lipids are held together in a bilayer structure by amphiphilic interactions, with protein thicknesses usually similar to the bilayer's unperturbed thickness. Since distinct proteins generally span distinct hydrophobic thicknesses and lipid composition can yield heterogeneity in unperturbed bilayer thickness, proteins induce lipid bilayer thickness deformations. Membrane protein may also curve the lipid bilayer (deform the lipid bilayer's midplane) without perturbing the lipid bilayer thickness. The energy cost of these deformations depends on the protein shape, lipid composition, and mechanical properties of the membrane, and so the lipid bilayer can regulate protein function. With the bilayer material constants measureable by experiments, in the simplest model, membrane elasticity theory can capture the energetic cost of bilayer deformations and, thus, quantify the relationship between membrane protein function and lipid bilayer mechanics. For the past two decades, experimental advancements in resolving protein structure have taught us a great deal about protein shape. However, deformation energy calculations, historically, have largely assumed proteins to have rotational symmetry. We present, validate, and benchmark a boundary value method (BVM) for constructing non-perturbative analytical solutions of protein induced bilayer deformations due to the protein shapes suggested by structural biology. We then apply the BVM to systematically survey the dependence of bilayer thickness deformations on protein shape, the relative stability of protein shapes, and the stability of oligomers. Our work was published in the academic journal Physical Review E. Alternatively, you can view an brief overview of our work through a poster I created and presented at a Computational Biology Symposium at the University of Southern California, Los Angeles, California .