You would not use kinematic equations, you would use Maxwell's Equations and model the behavior of the charges in the bulk by the permittivity and permeability. This is a rather complex process though. If you are talking about the electrostatic case, then we use Poisson's Equation to find the potential, charge, and electric field distributions. If we are talking about electromagnetic waves, then we would use the full Maxwell Equations. The process to find the charge and current densities depend upon the material and geometry of the specific problem. This can be done in closed form for a small set of problems but in general we use computational electromagnetic solvers like the method of moments, finite difference time-domain, or finite element method to solve for the current and charge distributions.
As for preventing wave propagation, any loss in the material would cause this (dependent upon the thickness of the material with respect to the wavelength). In general, any good conductor, like gold, silver, copper, aluminium, have high enough conductivities that most RF and microwave electromagnetic waves are prevented from propagating. Low frequency waves (say kilohertz and below) will take a rather thick block of even a good conductor to extinguish. And for frequencies in the Terahertz range and above, there are additional physics like plasmonics and quantum that dictate the transparency of the material.