Until recently, the design and analysis of block-type machine foundations did not properlyrnconsider impedance functions. This thesis aims at incorporating impedance functions byrnmaking use of recently compiled closed form expressions and dimensionless graphs for thernpurpose of determining dynamic stiffness and dashpot coefficients. Based on thesernexpressions and the well-known solutions of the dynamic equations of motions, a computerrnprogramme is written in FORTRAN.rnThe general requirements and criteria to be fulfilled for machine foundations are compiled.rnThe input soil parameters essential for the design including shear modulus, G, Poissonâ€™srnratio, , damping ratio, D, spring stiffness K, and shear wave velocity, Vs, are reviewed.rnThe basic concepts in vibration of structures like frequency, free vibration (undamped andrndamped), forced vibration and foundation vibration are discussed. In addition, thernperformance requirements and the basic steps employed in the design of a machinernfoundation are presented. The older approaches of machine foundation analysis are alsornreviewed.rnThe basic steps and relations used to calculate the uncoupled vertical and torsional vibrationrnamplitudes as well as the coupled rocking and horizontal vibration amplitudes are provided.rnxrnBased on the basic relationships for the vibration amplitudes and the relatively simplified andrnwell-compiled recent works of G. Gazatas [2] for the determination of static stiffness,rndynamicrnfoundation soil stiffness as well as radiation dashpot coefficient, a computer program inrnFORTRAN is written to analyze block-type machine foundations for the following fourrnconditions in a rational approach.rn(a) Foundation on the surface of a homogeneous half spacern(b) Partially of fully embedded foundation in a homogeneous half space.rn(c) Foundations on the surface of a homogeneous stratum overlying the bedrock.rn(d) Partially of fully embedded foundations in a homogeneous stratum overlying the bedrock.rnFinally, practical examples are solved for the above four cases using the programme and thernresults are checked against each other. The same example is also solved using the classicalrnmethod even though this method does not appropriately incorporate the impedance functions.rnA comparison of the results obtained using the classical approach and the more rationalrnmethod adopted in this work indicates that the latter is a substantial improvement over thernformer. A comparison of the results obtained showed that embedding a foundation is a veryrneffective way to reduce to the acceptable levels of the anticipated amplitudes of vibration,rnespecially if these amplitudes arise due to rocking or torsion. Such an improvement would berneffected mainly by the increase in radiation damping produced by waves emanating from thernvertical sidewalls.