In our previous paper (Bulletin of the Karaganda University. Chemistry series, 2019, 2(94), P. 35-43) we considered the behavior of quenched (or strongly charged) polyampholytes based on fully charged anionic monomer - 2-acrylamido-2-methyl-1-propanesulfonic acid sodium salt (AMPS) and cationic monomer - (3-acrylamidopropyl) trimethylammonium chloride (APTAC) in aqueous-salt solutions. In the present paper we report the mechanical properties of quenched polyampholyte hydrogels synthesized by free-radical copolymerization of the same monomers in the presence of N,N-methylenebisacrylamide (MBAA) as crosslinking agent. The hydrogel samples in dependence of the molar amount of AMPS were abbreaviated as AMPS-75H, AMPS-50H and AMPS-25H. The swelling, rheological, and mechanical properties of quenched polyampholyte hydrogels were evaluated for different compositions of copolymers at fixed initial monomer concentration C-0 = 0.5 wt.% and constant amount of [MBAA] = 20 mol.%. The formation of hydrogels in the course of (co)polymerization of oppositely charged monomers in presence of MBAA was monitored by rheometric measurements using oscillatory deformation tests at an angular frequency omega = 6.3 rad.s(-1) and strain amplitude gamma(o) = 0.01. The strain-stress curves of as-prepared and swollen polyampholyte gels demonstrate that the highest values of Young's modulus E, fracture stress sigma(f) and elongation epsilon% are characteristic for as-prepared AMPS-75H and swollen AMPS-50H samples. These results are interpreted in terms of polyelectrolyte and polyampholyte effects.