Modal analysis is widely used to validate numerical models, for quality control in manufacturing, and to detect structural damage. However, it is hard to compute modes of a structure with cracks, because the partial differential equations used in continuum mechanics are undefined along discontinuities in the deformation field. Peridynamic theory is a nonlocal extension of continuum mechanics that uses integral equations, which are defined in presence of cracks. Therefore, it is can be used to analyze changes in natural frequencies and mode shapes due to cracking. In this study, we compute the first five modes of 3D isotropic plates made from poly(methyl methacrylate) with free-free boundary conditions in peridynamics and compare them to experimental and finite-element analysis results. Afterwards, we introduce a crack in the cross-section and again compare the peridynamic and experimental results. Peridynamic natural frequencies of both healthy and cracked plates are within 3% of the experimental results and show similar frequency shifts due to damage. PD mode shapes match the experimental ones in both healthy and cracked cases.