Abstract: A spherical stress wave generator was developed, which included a central initiating explosive charge designed in the shape of a mini-spherical with yield equivalent to 0.125 g TNT. The scale of the generator was Φ1370 mm×1200 mm. The propagation medium of the stress wave for this generator was the remolding loess whose density is 1.8g/cm³, the degree of saturation is 22%. The circular electromagnetic particle velocity gages were directly embedded into the remolding loess on the central plane to measure the particle velocity profiles generated by explosion. In order to supply the reliable supporting data to the FEM numerical simulation of underground explosion, the Lagrangian analysis to the particle velocity profiles was executed to obtaining the constitutive equations of the remolding loess in the viscoelastic zone. The theoretical derivation and solving process of Lagrangian analysis based on one dimension spherical symmetry were introduced in detail. The strain, stress and strain ratio profiles were obtained through Lagrangian analysis for a set of particle velocity profiles. The hysteresis curve of stress-strain to the loading and unloading processes was obtained. Some difficulties about how to establish path lines were discussed.