Cementing is an extremely important part of completing an oil and gas well. Based on quality and type of cement used, factors such as the future exploitation of the well and its ability to withstand changes in temperature and pressure are evaluated. The important mechanical properties such as Young''s modulus, Poisson''s ratio, bulk modulus, shear modulus and constrained modulus are discussed in this thesis. Static and Dynamic testing are two methods to measure the mechanical properties of cement slurries. These tests are important in predicting the quality and integrity of the cement sheath during the life of the well. In general, the thesis describes the static and dynamic models used to calculate parameters and analyze results obtained during testing in order to determine the strength of the cement sheath under typical operating conditions. The estimated compressive strength found using dynamic methods (Mechanical Properties Analyzer, Ultrasonic Cement Analyzer) is compared with unconfined compressive strength found using static measurements (load frame testing methods).