Hydrogels, water-saturated polymer networks find widespread use in soft robotics, biomedical, pharmaceutical and food industries. Both solid and water constituents of hydrogels are sensitive to external stimuli such as temperature, humidity, osmolarity, and light. For instance, common hydrogels swell or shrink in the presence of chemical potential gradient between the sample and surrounding environment. Corresponding changes in internal water content lead to significant changes in mechanical properties of hydrogels. Besides, internal stresses build up if the gel samples are constrained during swelling or dehydration. In the present research, we utilize modal analyses technique on drying hydrogels to identify dehydration-induced changes in elastic moduli and internal stresses. In particular, natural frequencies and damping ratios of the first two axisymmetric transverse vibration modes are measured on clamped gelatin disks using non-contact laser vibrometry at various water loss states. Experimental modal frequencies are then compared to the predictions of a pre-stressed thick plate model. The evolutions of elastic moduli and internal stresses for water losses up to 80% are identified. The broadband loss capacity of gelatin is also determined from the measured modal damping ratios. Highly transient mechanical response observed on the gelatin disks further demonstrates the need for non-contact and rapid mechanical characterization of hydrogels. As illustrated in this work, vibration and wave-based techniques are promising candidates to fulfill that need.