Due to surface tension, a liquid drop below the capillary length scale naturally forms a spherical cap on solid surfaces. Drops on solid surfaces are denoted as sessile drops to distinguish from spherical drop without liquid-solid contact. When a sessile drop is disturbed, surface tension restores the drop's partial spherical profile. Surface tension thus arms the liquid-gas interface as a spring. If one further considers the drop's mass and viscosity, then sessile drops can be identified as a mass-spring-damper system. The mechanical response of a drop reflects the three aspects of the system, and this experimental study mainly investigates these different aspects by probing the static and dynamic response of sessile drops using quasi-static and oscillatory forcing. This experimental study focuses on the resonance of mechanically vibrated sessile drops and then extends to the mechanics of water balloons. Shape, frequency and amplitude responses of resonating sessile drops are first examined for individual modes. To characterize the observations, different aspects of experiments are related to Rayleigh-Lamb[90, 62], Bostwick-Steen inviscid[10] and Bostwick-Steen viscous potential flow (VPF)[16] theories. Observed mode shapes are related to predictions from Bostwick-Steen inviscid theory via ray-tracing simulation. Frequency responses are compared to all three theories, with Bostwick-Steen VPF theory best matching experiments as it includes both the presence of substrate and weak viscosity of drops. The observed amplitude responses of harmonic and subharmonic modes are qualitatively explained by nonlinear spring models, and a frequency-matching technique is demonstrated to trigger superharmonic modes. Further exploration reveals the interactions of modes such as spectral crossing and mode mixing, from which a mode separation technique is developed. For subhemispherical drops, typical observations are mixtures of a half-frequency subharmonic non-zonal mixing a harmonic zonal mode. For superhemispherical drops, more diverse mixing phenomena are discovered by preliminary observations. The investigation is extended to membrane-covered drops, or balloons. As it turns out, balloons can resemble purely liquid sessile drops in many aspects. When quasi-statically inflated, the balloons may or may not respond monotonically, and the response is adjustable via material properties and other parameters. When vibrated, these balloons exhibit several mode shapes similar to those of vibrated sessile drops. In fact, a one-to-one correspondence exists between mode shapes of drops and balloons, and therefore for these tests, balloons are technically drops equipped with a much higher effective surface tension.