This thesis describes a new instrumental approach designed to measure the complex Young’s modulus on cylindrical samples 1 inch in diameter 2 inch long and typically in the range of 1-70 GPa. Excitation frequencies are from 11 Hz to 167 Hz. The setup is based on the Forced Deformation Method (Batzle et al., 2006) and is capable of measuring phase and magnitude of the dynamic stress and strain. An actuator provides an oscillating force from one end of the plug. Strain is measured on the cylindrical side with three strain gages evenly spaced around the circumference. The lowest recordable magnitude of strain is in the order of 10E-8. Force is measured by a piezoelectric transducer. Values are < 10 N. Plug sample measurements of the Young’s modulus values for Berea sandstone, Castlegate sandstone, Pierre shale, PEEK, and aluminium alloys (ALU-7075 and ALU-6061) are included. Reference material results are in accordance with published values. Some of the instrumentation needed is also given in detail in the previous work (Fintland, 2010).