This paper analyzes the dynamic response of fixed supported orthotropic plates under localized blast loading using the method of modal superposition. The analysis procedure is used to quantify the linear transient response of such plates to the localized blast load at different positions. Many studies are currently available, in which the blast load is considered to be spatially uniform across the plate, with a temporal distribution described by a Dirac delta function. The novel aspect considered here is the case for which the blast load is modeled as a linear triangular function, and the orthotropic plate is fixed along its edges. A Mathematica program is used to solve the first and the second auxiliary Levy-type problem to determine the values of the natural frequencies of the system. The results presented here are collected from the results of analyses performed on localized blast-loaded orthotropic plates, for a variety of parameters important with regard to the dynamic response. Conclusions are drawn concerning the influence of the various parameters on the nature of the orthotropic-plate response.