The validity of the affine assumption in model flexible polymer networks is explored. To this end, the displacements of fluorescent tracer beads embedded in polyacrylamide gels are quantified by confocal microscopy under shear deformation, and the deviations of these displacements from affine responses are recorded. Nonaffinity within the gels is quantified as a function of polymer chain density and cross-link concentration. Observations are compared with current theories of nonaffinity in random elastic media. We note that the mean-squared nonaffine deviation is proportional to the square of the applied strain in the linear elasticity regime, as per theoretical predictions. The measured degree of nonaffinity in the polyacrylamide gels suggests the presence of structural inhomogeneities which likely result from heterogeneous reaction kinetics during gel preparation. In addition, the macroscopic elasticity of the polyacrylamide gels is confirmed to behave in accordance with standard models of flexible polymer network elasticity.