An inverse geometry heat conduction problem (shape identification problem) is solved to detect the unknown irregular boundary shape by using the boundary element method (BEM)-based inverse algorithms. They are the Levenberg-Marquardt method (L-MM) and the conjugate gradient method a (CGM), respectively. A sequence of forward steady-state heat conduction problems is solved in an effort to update the boundary geometry by minimizing a residual measuring the difference between actual and computed temperatures at the sensor’s locations under the present two algorithms. Results obtained by using both schemes to solve the inverse problems are compared based on the numerical experiments. One concludes that the conjugate gradient method is better than the Levenberg-Marquardt method since the former one : (i) needs very short computer time; (ii) does not require a very accurate initial guess of the boundary shape; and (iii) needs less number of sensors. Finally the effects of the measurement errors to the inverse solutions are discussed.