We propose a version of the 2D Regge calculus, in which the areas of all triangles are equal to each other. In this discretization Lund-Regge measure over link lengths is simplified considerably. Contrary to the usual Regge models with Lund-Regge measure, where this measure is nonlocal and rather complicated, the models based on our approach can be investigated using the numerical simulations in a rather simple way. (c) 2005 Elsevier B.V. All rights reserved.