The materials investigated were silicon carbide foams of various densities ranging from 7.7% to 12.3% of the bulk material density. They were characterized under pure shear and uniaxial compression. Special test procedures were developed for this testing. For shear characterization two pairs of prismatic strips were used in a three-rail fixture. Stress-strain curves to failure were obtained from which the shear modulus, shear strength and ultimate shear strain were determined. A statistical analysis based on the Weibull distribution function was conducted to determine expected differences in results obtained by different test methods, specifically differences between three-rail shear and torsion test results. A power law model was proposed to describe the variation of shear modulus with relative density. It was also shown that the parameters of this model depend on the porosity structure of the foam for the same density. Similar tests were conducted under uniaxial compression. It was found that the Young's modulus varies linearly with the relative density of the foam.