Elasticity of nonionic and weakly ionized acrylamide-based hydrogels was studied as a function of swelling degree Q and initial total monomer concentration c(0). The sheer modulus decreases as Q(-m) at low Q and then increases steeply because network chains no longer obey Gaussian statistics. The exponent m decreases from 0.7 to 1/3 as c(0) increases from 5 to 30 wt %. Ionization of network lends to a decrease in the modulus, and this effect disappears at high concentrations of added salt, as predicted by a recent model. At swelling equilibrium, the modulus provides an "effective" measure of the osmotic pressure. The upturn in the modulus is described using the inverse Langevin function that allows estimation of an average network chain length. This length was compared with that of a perfect network chain, and the network density was evaluated from the modulus in the preparation state. This indicates that networks prepared with low c(0) contain a large amount of elastically ineffective segments. Their "chains" apparently have architecture typical of ideal random-branched macromolecules without loops. At high c(0), "effective" perfect networks with insignificant number of interchain trapped entanglements are formed.