Measurements were made of the dynamic flexural modulus, dynamic Young’s modulus, damping, strain amplitude, and the strain amplitude dependence of damping in iron/copper- and steel-based metal matrix composites. Comparisons were made concerning the steel matrix specimens before and after heat treatment. The flexural modulus tests were performed using the Grindosonic technique, while the Young’s modulus, damping, strain amplitude, and the strain amplitude dependence of damping were determined using the piezoelectric ultrasonic composite oscillator technique (PUCOT). Metallographic studies utilizing chemical etching, optical and electron microscopy, and microhardness testing were performed to assess the distribution of the fibres in the composites. The variation of dynamic Young’s modulus with respect to percentage copper in the composites followed the rule of mixtures.