Underground energy storage (UES) in porous and cavity reservoirs can be used to balance the mismatch between the production and demand of renewable energy, as well as for securing gas and oil supply during shortage or high demand periods. Understanding the geomechanical behavior of these reservoirs under different storage conditions, i.e., storage frequency and fluid pressure, is key in defining their capacity and effective lifetime. This thesis work presents a rigorous analysis performed on sandstones to unravel their geomechanical response under cyclic loading. This study includes, importantly, both experimental and numerical investigations under several conditions which are relevant to UES. The rock response was studied considering cyclic stress states above and below the onset of dilatant cracking, under different frequencies and amplitudes. Within the number of cycles studied, measurements of axial strains and acoustic emissions indicated that inelastic strains accumulated cycle after cycle following an exponentially decreasing rate. Five types of deformations were interpreted: elastic, plastic, viscoelastic, cyclic-plastic and brittle creep. Based on these novel experimental results and observations, Nishihara's constitutive model was used for simulating viscoelastic and brittle creep deformations, while dilatant plastic strains were modeled using a Hardening-Softening model. Finally, an extension of the Modified Cam-Clay model was proposed to account for cyclic-plastic compaction. This approach can be extended and improved to study cyclic sandstone deformation's implications on subsidence, fault reactivation and cap rock flexure, among other physical phenomena impacting a reservoir's storage capacity.