A time-variant similarity transformation model has been proposed recently for reference frame transformations across time. It has been postulated that reference frame variations only result in uniform deformations (i.e.by the same scale factor in all directions). However, this is not always the case in a deforming area. In this study, a time-variant affine transformation is proposed to accommodate possible non-uniform deformations for reference frame applications in a significantly deforming area. This model also enables the investigation of the deforming behaviour of a reference frame with physically interpretable parameters. To prove its feasibility for present day reference frame applications, numerical tests are performed on an actual data set from the continuous GPS stations in Taiwan. Results illustrate a substantial improvement in the quality of reference frame transformations when the proposed approach is implemented.