Alginate hydrogels have been attractive for a variety of biomedical applications, but they possess limited mechanical properties when ionically cross-linked with divalent cations. Therefore, covalent cross-linking of alginate with poly(ethylene glycol)-diamines of various molecular weights was investigated as a means to generate hydrogels with a range of mechanical properties. Hydrogels with a range of elastic moduli could be generated by controlling either the chain length of the cross-linking molecule or the cross-linking density. The elastic modulus increased gradually with an increase in cross-linking density or weight fraction of PEG in the hydrogel up to similar to 27% (w/w) of PEG. The change of mechanical properties was interpreted in terms of molecular weight between cross-links (M-c) according to the rubber-elasticity model, and the results of this analysis were generally consistent with the measured PEG-diamine incorporation efficiencies in this range. However, as the weight fraction of PEG in the hydrogels increased above 27%, regardless of the molecular weight of PEG, the elastic moduli decreased. This is not consistent with prediction based on the rubber-elasticity theory, and this is likely due to the fact that this model does not consider cross-linking with a second macromolecule. Importantly, the results of this study suggest that the mechanical properties of hydrogels will be strongly affected by the properties of the cross-linking molecule as the M-c of hydrogels falls below the molecular weight of the cross-linking molecule.