Numerical techniques are presented for extending and implementing the Lagrangian analysis originated by Fowles, Williams, and Cowperthwaite. The analysis derives internal energy, specific volume, and stress and particle velocity histories from either stress or particle velocity records from a series of gages embedded in material undergoing uniaxial strain flow. The material may have an arbitrarily complex constitutive relation. The accuracy of the analysis for attenuating waves is studied by handling analytically derived stress and velocity histories. Waves with attenuation of 40–75% can be treated, depending upon the accuracy desired. The analysis is applied to waves measured in graphite, sandstone, asbestos phenolic composite, and porous alumina.