Seismic tomography traditionally inverts for velocity field on a regularly spaced and fixed-in-space model grid. Such an approach is not able to adequately describe pinchouts or wedge-shaped velocities as commonly seen at basin boundaries, faulted rock beds, and back-arc mantle wedges. A regularly spaced model grid also requires the use of a large number of model variables. This paper shows a different approach called deformable layer tomography (DLT) to directly invert for velocity interfaces. The use of thickness-varying layers allows a much smaller number of model variables for the DLT than the regularly spaced model grid. In the DLT the geologic framework and known velocity range are adopted into the initial reference model, and the best-data-fitting geometry of the velocity interfaces is determined, as illustrated by synthetic and field data examples.