Results are presented for the preliminary mechanical design of a light ion beam Laboratory Microfusion Facility (LMF). Applications of the facility include the development of high gain, high yield ICF targets. The LMF target chamber must meet the requirements imposed by the ion beam propagation, and survive severe target blast loadings. Yields from 10 to 1000 MJ are considered for a projected lifetime of up to 15,000 shots. The chamber will be subjected to repeated loadings that include intense x-ray vaporization of the first wall surface, resulting in large amplitude pressure waves. A carbon/carbon composite thermal liner has been proposed to attenuate the radial shock waves and protect the structural wall. Nevertheless, the chamber wall must still be designed to withstand large impulsive and residual pressures. The proposed target chamber consists of a capped cylindrical shell that is 1.5 m in radius and 4.5 m in height. The analysis of the mechanical response of the structural wall from the repetitive dynamic overpressures is described in detail. Modified elastic constants are used to account for the higher ligament stresses and strains which are present between the beam ports and diagnostic ports. In addition, fatigue lifetime calculations have been made according to ASME guidelines, applying cumulative damage criteria specified by Miner's rule. A modified rainflow cycle counting method was used in conjunction with Goodman diagrams to determine equivalent stresses and strains to be used with the constant amplitude, fully reversed fatigue data. Both 6061-T6 aluminum and 2 1/4 Cr - 1 Mo steel are considered for the structural materials, with maximum stress and fatigue design results developed for a range of thicknesses and overpressures.