The development of sophisticated kinetics theory model of a reflected reactors which comprising core and reflector regions has been considered. Within each region, the theory is space-independent and assumes one energy group. A detailed investigation of both mathematical and numerical solutions has been conducted and applied to the two-point kinetics for reflected reactors using the Analytical Inversion Method (AIM), which permits a fast inversion of polynomials by going temporarily to the complex plane. This method has been tested using two types of reflected reactor systems: the experimental zero-power reactor (PROTEUS) and a large tightly coupled system with a small homogeneous core surrounded by a series of non-multiplying reactors (AGN-201). In addition, an economical general approximate expression to the exponential function for the two-point kinetics matrix is derived and Pade Β΄rational approximations of different types are applied. In order to ensure the validity and stability of this method, the numerical results obtained with this algorithm are tested on a set of four kinetic problems, step, ramp, zigzag and oscillatory of reflected reactors reactivity change under considerations.