The present work is concerned with the effective numerical implementation of the adaptive dual boundary-element method (DBEM) for two-dimensional elastic problems. The method uses a simple error estimator, based on the discontinuity of the solution across the boundaries between adjacent elements and implements the h version of the adaptive mesh refinement for 2D elastic BEM formulation. In order to validate the algorithm, four problems are solved: two classical elasticity theory examples and two from fracture mechanics. To demonstrate the algorithm effectiveness, these problems are solved using both conventional BEM and DBEM and its adaptive forms.