Safety is one of the most important issues regarding tunnel construction. During the construction, the highest degree of collapsing risk is present in the unsupported area in front of the tunnel's working face where the newly dug cross section hasn't been supported yet. In order to provide safe working environment and withstand falling out of blocks, a temporary support measure called pipe roof is bored into the working face surface. Within the tunnel constuction technology, various methods are being used to design the load-bearing steel elements, but they are not necessarily optimal. Based on the in-situ measured displacements obtained during the construction of Trojane tunnel, it is possible to assess the curvature of constructed pipe roof. These values are transferred to bending moments along the element. In the thesis, the existing methods of design are presented, yet proven to be uneconomical. Therefore, a new empirical method which considers real deformational behaviour of tunnel is developed based on the determination of the displacement function. A specimen of measure values is used for curve fitting. Thus, a uniform function of displacements can be used to calculate bending moments without any major assumptions of material, load or statical model (as opposed to existing methods). As an alternative, a method based on the Pasternak's model of a beam on the elastic support is studied. Both existing and newly developed methods are programmed in the MATLAB environment to enable the comparison of design values with the measurements from the Trojane tunnel. Empirical method using the displacement function theory is proven to precisely approach measurements and thereby assure both the safest and the most economical way of designing the pipe roof.