The response of the engineering system is often obtained by the use of numerical methods such as finite element method or boundary element method. However, the uncertainty of the acquired solutions cannot be measured using conventional methods. This uncertainty is attributed to two sources: errors in mathematical modeling and uncertainties in the parameter. The following paper addresses the second source of uncertainty for the steady state heat conduction problem where the material conductivity is uncertain. Material uncertainty is implemented into fuzzy boundary element method which obtains the exact worst case bounds on the response given the worst case bounds on the parameter uncertainty. The method assumes that a correct partial membership function is given. Numerical examples are shown to illustrate the behavior of the method.