Tolerance analysis of auto body requires the consideration of its compliance because of potentially significant deformation during the spot-weld assembly process. In this paper, a relatively recent method for such analyses is briefly introduced as one can find in the literature. In this method, it is important to take into account of the covariance between the sources of variation as they are closely located, which is the case in most auto body assembly. However, it is often impossible to know such covariance, for example, when a new car is being developed. Therefore, a mechanics-based method is proposed in this paper to estimate the covariance among the sources of variation by finite element analyses and simple statistical computations. The proposed method is illustrated by applying it to a three-dimensional model of real front wheel housing.