This study investigates the benefit of coating silicon-substrate microelectrode arrays with hydrogel material for improved biocompatibility. Varying coating thicknesses and hydrogel material descriptions were considered to determine the impact on reducing strain in the surrounding brain tissue caused by relative micromotion of the electrode. Finite element simulations were used to explore biocompatibility by focusing on the longitudinal micromotion of an implanted single electrode shank. The finite element model for the brain and electrode, both with and without the hydrogel coating, remained constant. Three constitutive models were considered to describe the brain and/or hydrogel material: linear elastic, hyperviscoelastic, and fractional Zener. All combinations of these three material descriptions were explored. The simulation results showed that the constitutive model, electrode coating thickness, and the degree of microelectrode adhesion to the brain influenced the maximum principal logarithmic strain and also the maximum electrode displacement. Biocompatibility was improved as evidenced by a reduction in the magnitude of strain in the brain when (i) a hydrogel coating was applied to the silicon electrode, (ii) the thickness of the hydrogel coating was increased, and (iii) the brain adhered completely to the hydrogel coating. A decrease in microelectrode displacement may be a useful metric for assessing an improvement in micromotion reduction.