Nonlinear deformations in fingerprint images, arising from the elasticity of the skin as well as the pressure and movement of the finger during image acquisition, lead to difficulties in establishing a match between multiple impressions acquired from the same finger. One solution to this problem is to estimate and remove the relative deformations prior to the matching stage. In this paper, these relative deformations are represented as an average deformation model based on minutiae locations and orientations using 2-D Thin Plate Splines (TPS). The estimated average deformation is used to pre-distort a template prior to matching it with a query image in a verification task. Experimental results show that the use of minutiae locations and orientations to estimate the deformation leads to a more representative deformation model than using minutiae locations only. An index of deformation based on the bending energy is also proposed to select templates with the least variability in the deformations. The EER goes down by ≈ 1:1% when we incorporate minutiae orientation information and use the template selection strategy.