An adaptive procedure in finite element analysis is presented for two-dimensional plane stress-strain and axisymmetric problems based on a modified strategy for h-refinement of meshes with quadrilateral and other shaped elements. The strategy suggests refinement levels to which a particular element has to be refined to obtain an acceptable level of accuracy in a single trial. A new refinement algorithm is presented for computer implementation. The use of a relational database management system for software development as an alternative to conventional data structures is illustrated. In the h-p refinement strategy used in this work, the adaptive h-refinement is followed by uniform p-refinement. The efficiency of the h-p refinement procedures and the software are illustrated through a number of examples. © 1993.