A multi-tensor model with identifiable parameters is developed for diffusion weighted MR images. A new parameterization method guarantees the symmetric positive-definiteness of the diffusion tensor. We set up a Bayesian method for parameter estimation. To investigate properties of the method, Monte Carlo simulated data from three distinct DTI direction schemes have been analyzed. The multi-tensor model with automatic model selection has also been applied to a healthy human brain dataset. Standard tensor-derived maps are obtained when the single-tensor model is fitted to a region of interest with a single dominant fiber direction. High anisotropy diffusion flows and main diffusion directions can be shown clearly in the FA map and diffusion ellipsoid map. For another region containing crossing fiber bundles, we estimate and display the ellipsoid map under the single tensor and double-tensor regimes of the multi-tensor model, suitably thresholding the Bayes factor for model selection.