The first main achievement is the expansion of the utilization of simple computational model for transverse displacements computation from single element to frame type structures. For this purpose a new finite element has been derived that overcomes the limitations of the analytical solution of the differential equation. To complete this, a huge database was established which will serve for the estimation of the adequateness of the definitions of the rotational spring, known from the references. If the comparison of the results shows that known functions are not adequate the obtained database will provide a platform for the derivation of a new, genuine definition of the rotational spring. The second main achievement was the expansion of the simplified computational model to the computation of transverse displacements due to tensile axial load in the single sided cracked elements. This covered the phenomena totally neglected in the references. The new model proved itself to be accurate enough as the comparison of the results of the two models, discrete but yet time consuming and consequently inappropriate for the inverse identification, and the simplified, showed that the maximum error in displacements lies with 5 %, which is completely acceptable from the engineering point of view. As the prime scope of the inverse identification is primarily to detect the presence of the crack, further to locate it, and finally, to estimate its severness, it can be concluded that the developed computational model can be successfully implemented in the inverse identification.