Abstarct: The process of heat transfer usually described by parabolic models. In some cases, when heat conductivity coefficients depend on the solution itself, the structure and properties of the solution changes significantly. If the elapsed time of heat transport process is very small the inertia starts to be important and the wave nature of the heat energy transport becomes a dominant process. For example, the physical phenomena involved in ultra-short laser pulse interactions with solids are very complex. It is shown that the classical parabolic two temperature model, which is baxsed on Fourier’s law, is not sufficiently accurate. For such cases, hyperbolic model has been suggested. Several strategies can be applied to construct numerical algorithms for finding solutions of the hyperbolic heat transport models. If the boundary conditions (heat flux or temperature distribution) on the surface are entirely known as a function of time and location, then temperature distribution inside the object can be determined by solving the heat transfer equation. This kind of problems called Well-posed. But many practical cases of heat transfer cannot be solved directly due to unknown boundary conditions (Ill-posed). Ill-posed problems can be solved by inverse analyses. One Procedure to solve Inverse heat transfer problem (IHCP (is to derive surface heat flux and temperature distribution from temperature’s change inside subject. In this thesis IHCP are solved by applying Conjugate Gradient Method (CGM). CGM method is baxsed on minimizing the sum of squared difference between the measured temperature and the calculated temperature. In order to demonstrate the experimental temperature, results of analytical method with adding a normal distribution are used. The method proves to be very useful and powerful especially when a direct measurement of surface heat flux and temperature is difficult to obtain, owing to several working condition. The thesis reviewed here, discussed one dimensional inverse heat conduction problem. Procedure, criteria, methods and important results of other investigation are briefly discussed. For The efficiency and accuracy of such algorithms are investigated by solving test problems.