Based upon the upper bound limit analysis, the stability numbers have been developed for a two-layered soil slope both for an associated flow rule material and for a homogeneous slope with non-associated flow rule material. The failure surface was assumed to be an arc of logarithmic spiral and it automatically ensures the kinematics admissibility of the failure mechanism with respect to the rigid rotation of the soil mass about the focus of the logarithmic spiral. The effect of the pore water pressure and horizontal earthquake body forces was also included m the analysis. For a non-associated flow rule material, the stress distribution along the failure surface was developed with the assumption of interslice forces given by Fellenius and Bishop. The stability numbers have been found to reduce appreciably with increases m the (i) horizontal inclination (β) of slope, (ii) pore water pressure coefficient, ru and (iii) horizontal earthquake acceleration coefficient (kh). The values of the stability numbers for a non-associated co-axial flow rule, with dilatancy angle ψ =0, have been found to be considerably lower as compared to the associated flow rule material. For a given height of the slope, with associated flow rule, the values of the stability numbers have been found to increase with increase in the thickness of a layer with greater value of the friction angle Φ. The results have been given in the form of non-dimensional stability charts, which can be used for readily obtaining either the value of the critical height or the factor of safety The methodology can be easily extended even for multi-layered soil slopes with different values of cohesion (c), bulk unit weight (γ) and friction angle (Φ). An attempt has also been made in this thesis to study experimentally the effect of the frequency of the excitation and the addition of non-plastic fines on the liquefaction resistance of the material Shake table studies, generating uni-axial sinusoidal horizontal vibrations, were earned out for this purpose. During the period of excitation of the material, the settlement at the surface of the sample increases continuously with time up to a certain peak value and thereafter, it becomes almost constant. For the excitation of the material with higher frequency, more number of cycles was seen to reach the final settlement. With the continuous excitation of the material, the magnitude of the pore water pressures increases up to a certain peak value and there after, its magnitude decreases till it again becomes the hydrostatic pressure as it was before the excitation of the material. The peak magnitude of the pore water pressure tends to be higher for the excitation with smaller frequency especially at greater depths from the ground surface. The addition of non-plastic fines tends to increase the magnitude of the settlement as well as the increase in the pore water pressure.