The new model proposed in this paper is the hidden Markov mesh model or simply the 2D HMM with the causality of top-down and left-right direction. With the addition of the causality constraint, two efficient algorithms for the evaluation of a model and the maximum likelihood estimation of model parameters have been developed which are based on the forward-backward algorithm. It is a highly natural extension of the 1D HMM and more intuitive than other 2D models. The proposed method will provide a useful way of modeling spatially distorted image patterns such as offline handwritten characters.