Foundations design considers ground properties in their natural state. However, the ground over which the foundation is based may be too hard or non-uniform. In the first case it might transfer too much vibration, and in the other case it can lead to differential settlements and lack of stability. A possible way of controlling vibrations radiation caused by machines, vehicles and trains and isolating structural vibrations is replacement of the original ground by layers of elastic media. The isolation of vibration amplitudes should be kept within the limits specified in standards, at the control points. Control of structural deflections can help in reducing or eliminating differential settlements and instabilities, which cause damage to structures or rotation like that of Pisa tower (12(th) century). The later was repaired just lately. Solutions in soil mechanics that are based on local elastic layering use certain specific kinds of elastic soils. Mostly the design involves replacement of the rock under the foundation by soft elastic soil, but there is also a possibility of excavating part of the underground hard rock and adding a very elastic filling instead. The paper investigates design configurations of such isolation and deflection controls by using computational simulations. The simulations are based on the finite difference method, where the rock/soil model is elasto-plastic, using known data for the elastic layer rock and concrete. The excitation data is based on measured information. The "half space" ground is "cut" by using special vertical and horizontal boundary conditions. Finally, examples of practical cases are added to show the efficacy of the isolation.