An investigation has been carried out to examine the dynamic behavior of concrete plates subjected to localized blast loading. The concrete plate is modeled as a thin plate with finite dimensions sitting on an elastic three-parameter soil foundation model. The localized blast loading is expressed by using the Dirac Delta function for different value of the load’s position. The governing equation of the problem is solved using the modified Bolotin method for determining the natural frequencies and the wave numbers of the system. The orthogonal properties of Eigen functions are used to find the general solution of the problem. Special emphasis is focused on the mid-point displacements. The results obtained allow an insight into the effect of the load’s position, the thickness of the concrete plate on the response of the concrete plate under localized blast loading and indicate that the load’s position and the thickness of the plate can affect their overall behavior.