Dynamical evolution models of 361 extragalactic Fanaroff-Riley type II radio sources selected from the Cambridge 3CRR, 6CE, 5C6, and 5C7 Sky Surveys, as well as the Bologna B2, Green Bank GB, and GB2 Surveys, are presented. Their spectra, compiled mostly from the recent catalogs of radio sources and the available NASA/IPAC and Astrophysical Catalogs Support System databases, along with morphological characteristics of the sources determined from their radio maps, have been modeled using the DYNAGE algorithm and/or its extension (KDA EXT) for the hypothetical case of further evolution after the jet's termination. The best-fit models provide estimates of a number of important physical parameters of the sources, as (i) the jet power, (ii) the density distribution of the external gaseous medium surrounding the radio core and the jet propagating through it, (iii) the initial energy distribution of the relativistic particles accelerated at the shock fronts, and (iv) the age of the observed radio structure. Additionally, estimates of some derivative parameters are provided, e.g., the radio lobes' pressure, their longitudinal expansion velocity, the magnetic field strength, and the total energy deposited in the lobes. The observed spectra and their best-fit models are included. Finally, one of the useful applications of the above models is presented, namely a strong correlation between the ambient medium density and the rest-frame two-point spectral index available directly from the observed spectra.