[en] The purpose of the paper is to illustrate the finite element technique when applied to the elastic stress analysis of steel pressure vessels and heat exchangers. The method yields more realistic predictions for the stress distribution than the conventional methods do (as for example the ASME Boiler and Pressure Vessel Codes). The problem which arises when applying the finite element technique to the stress analysis of reactor pressure vessels and heat exchangers is, that the inclusion of the individual tubes and perforations in the supporting tube sheets in an extremely high computational effort. The way in which this problem is solved consists in performing the analysis in two steps. The first step is to analyse the entire reactor pressure vessel or heat exchanger by replacing the perforated plates by solid plates with the same stiffness behaviour and to idealize the tubing by a continuous elastic support. In this paper several finite element models for both the first and the second step, are investigated. (Auth.)