The structure and elastic moduli of end-cross-linked poly(dimethylsiloxane) (PDMS) networks are studied using molecular dynamics (MD). The systems consist of 2000 PDMS chains of length 20 monomers and 1000 chains of length 40 monomers with varying amounts of cross-linker molecules. The networks are formed dynamically within the MD simulations. Starting from an equilibrated melt, tetrakis(dimethylsiloxy)silane cross-linkers are attached randomly to a fraction of the chain ends. When a free end comes within a short capture distance from an unsaturated cross-linker, a bond is formed between the chain and the cross-linker. The kinetics of the cross-linking process are studied as a function of the stoichiometry of the number of cross-linkers and are found to agree with earlier predictions. Stress relaxation simulations are performed on the fully formed networks by straining each system at four different rates and recording the tensile stress during the relaxation period. Results for the elastic moduli of the networks calculated from the plateau value of the tensile stress are compared to network models, and qualitative agreement with dynamic mechanical experiments is found. The chain conformations after straining indicate that these networks are deformed much more affinely than what is seen experimentally.