The surface structure of supported nanocatalyst particles plays a significant role in the kinetics of fuel cell reactions. We present the results of molecular dynamic simulations of the structure of nanoparticles of platinum and several of its alloys, gold, cobalt, copper, iron, and rhodium. The simulations include the effect of a carbon substrate on the various bond orders (sums of spherical harmonics to form various invariant functions) and the strain-vector field. The strain-vector field (the set of displacement vectors between the atom locations at equilibrium and the reference state) shows the distortion in the nanoparticle as a result of interaction with the substrate. The effect of particle size on the strain-vector field observed throughout the nanoparticle is discussed. Effects on particle morphology of alloying elements and the nature of the support are discussed. Bond orders for atoms in the clusters were calculated to further understand the presence of a secondary Mackay transformation between the icosahedron and cuboctahedron morphologies. Geometric utilization of catalyst particles based on the change in surface area due to the change in shape of the particle is estimated. Application of the results from the MD simulations for HRTEM simulations and the design of new catalyst materials are discussed.