For about half of the known virus families, the coat that protects their genome in the form of DNA or RNA is a ‘spherical' or icosahedral capsid which is composed of many copies of individual proteins that must self-assemble correctly, rapidly, and reproducibly on a biological timescale in order to propagate an infection in vivo. Elucidating the self-assembly of empty viral capsids may have the potential to assist in developing novel approaches to interfere with viral infection. We have developed a geometric model that can mimic the basic shape and interface interactions of each capsid protein for use in conjunction with the rigid-body Monte Carlo simulation method and the discontinuous molecular dynamics algorithm - a fast alternative to standard molecular dynamics. This model has allowed us to simulate the spontaneous formation of multiple complete T=1 viral capsids simultaneously in relatively large systems containing many capsid proteins. Also, our simulation results are able to capture in general features of self-assembly as observed in experiments on a variety of viruses. Detailed analysis on the kinetics and thermodynamics of capsid self-assembly will be presented.