The aim of this work is to demonstrate a computational workflow for the generation of cross-linkable viscoelastic polymers and the determination of elastic and hyperelastic properties by means of all-atoms classical molecular dynamics simulations, using polydimethylsiloxane (PDMS) as an example. To improve the computational efficiency of the workflow, a phenomenological description of the cross-linking process is chosen instead of a quantum mechanical description of the cross-linking mechanism. The structures produced differ in their conversion degree of cross-linking (cdc) of 60, 70, and 80 percent and their quantity ratio between polymer chains and cross-linking units of 2 to 1 and 5 to 1. In order to exclude finite size effects of the molecular systems as much as possible, large systems of about 40,000 atoms are considered. Furthermore, for each possible configuration from the combination of cdc and the ratio of polymer chains to cross-linking units, six structures different from each other are used. Tensile and compression tests are performed to determine mechanical properties. A dependence of stresses in the deformation direction on strain rate is found for strain rates 107, 108, and 109 1/s. As the cdc increases, an increase in the stress values is observed in the tensile tests. To determine the viscoelastic material properties, relaxation tests are performed following the tensile tests. Thereby, the determined relaxed stresses after the tensile test rise with the increase of the cdc. Furthermore, no large stress deviations, .34 MPa maximum, between structures differing by chain to linker ratio are observed with the Ogden model. The computational workflow shows that classical all-atom molecular dynamics simulations can be a suitable method for structure generation and subsequent characterization of elastic and hyperelastic properties of cross-linked polymers.