This study is intended to provide a different perspective for solving two-dimensional inverse heat conduction problems. At the beginning of the study, finite-difference methods are employed to discretize the problem domain and then a linear inverse model is constructed to identify the initial and boundary conditions. The present approach is to rearrange the matrix forms of differential governing equation and estimate coefficients of unknown condition. Then, the linear least-squares method is adopted to find the solution. The results show that if the measurement errors are considered, more measuring points are needed in order to increase the congruence of the estimated results to exact solutions. In this paper, temperature-time Variations are measured at internal and outside points. A little effect of the measurement time interval on the estimates are shown with-the method proposed. (C) 1997 Published by Elsevier Science Ltd.