The mechanical properties of a polymeric network containing both crosslinks and sliplinks (entanglements) are studied using a multichain Brownian dynamics simulation. We coarse-grain at the level of chain segments connecting consecutive nodes (cross- or sliplinks), with particular attention on the Gaussian statistics of the network. Affine displacement of nodes is not imposed: Their displacement, as well as the sliding of monomers through sliplinks, is governed by force balances. The simulation results of stress in uniaxial extension and the full stress tensor in simple shear, including the (nonzero) second normal stress difference, are presented for monodisperse chains with up to 18 entanglements between two crosslinks. The cases of two different force laws of the subchains (Gaussian chains and chains with finite extensibility) for two different numbers of monomers in a subchain (n(o)=50 and n(o)=100) are examined. It is shown that the additivity assumption of slip- and crosslink contribution holds for sufficiently long chains with two or more entanglements, and that the assumption can be used to construct the strain response of a network of infinitely long chains. An important consequence is that the contribution of sliplinks to the small-strain shear modulus is about 2/3 of the contribution of a crosslink.