As the world continues to seek effective solution to nuclear disaster, it is of interest for us to join the search for the practical solution through Mathematics. In this work, the energy balance equations associated with nuclear technology were structured in parametric form as the basis for the Mathematical model solvable by the Conjugate Gradient Method (CGM) Algorithm. Consequently, Nuclear Reactor Safety was modeled in form of a quadratic functional. The nuclear tokens were structured and used as elements of the control matrix operator in the model. The numerical results obtained through the Conjugate Gradient Method (CGM) algorithm identify the optimal level of safety required for Nuclear Reactor construction at any particular situation. Furthermore, the residual parametric heat equations of nuclear reactors safety were transformed into control cost functional. The Existence and Uniqueness of the resulting control system were established. The results indicate that a lot can be done in the area of Optimization of nuclear safety. This book is very useful for the Mathematicians, Physical and Nuclear Scientists or any other Scientist interested in Nuclear Reactor Safety.