Equilibrium molecular dynamics simulations are used to obtain the pressure and configurational chain properties of near-perfect, off-lattice, trifunctional hard-chain networks of chain lengths 20, 35, 50, and 100, and of tetrafunctional hard-chain networks of chain lengths 20, 35, and 50 over a range of packing fractions. Our simulation results show that the variation of network pressure with density is similar to that of uncrosslinked chain systems of the same chain length, except at low densities where the network pressure shows a negative region, as first observed by Escobedo and de Pablo. We present a theoretical treatment leading to an analytical expression for the network pressure as the sum of liquid-like and elastic contributions. The liquid-like contribution is obtained by extending the generalized Flory-dimer theory to networks, and the elastic contribution is obtained by treating the network as a set of interpenetrated dendrimers and using an ideal chain-spring analogy to calculate the free energy. The theoretical predictions for network pressure are in good agreement with simulation data.