This chapter documents the procedure for determining viscoelastic and damage properties using a harmony search (HS) algorithm that employs a heuristic algorithm based on an analogy with music phenomenon. To determine the viscoelastic material parameters, the steps involved in conducting the interconversion between frequency-domain and time-domain functions are outlined, based on the presmoothing of raw data using the HS algorithm. Thus, a Prony series representation of the fitted data can be obtained that includes the determination of the Prony series coefficients. To determine the damage properties of hot mix asphalt (HMA) concrete, a rate-type evolution law is applied for constructing the damage function of the HMA concrete. The damage function can be characterized by fitting experimental results using the HS algorithm. Results from laboratory tests of uniaxial specimens under axial tension at various strain rates are shown to be consistent with the rate-type model of evolution law.