Purpose of this paper: In this paper we present a summary of the results reached in the field of computer tomography applied in some special case – for the problem of incomplete projection data. This particular problem arises in the technical issues in which, for some reasons (like for example size of the examined object, its localization or its accessibility), it is impossible to apply the standard algorithms of computer tomography. Design/methodology/approach: In the paper we discuss the standard algebraic algorithms of computer tomography and, additionally, the new algebraic algorithms (parallel and chaotic), designed by the authors, suitable not only for the case of incomplete projection data but also useful in the standard approach. Findings: The above mentioned algorithms are tested in solving the problems of reconstruction the discrete objects of high-contrast. Moreover, convergence, stability and utility of the algorithms are proved experimentally. Research limitations/implications: Algorithms, created by the authors, are designed for the multiprocessor computers which allow to execute the calculations simultaneously. However, the results compiled in the paper were elaborated by using the one-processor computer. Calculations in which the parallel computing structure will be used are planned for the nearest future.Practical implications: Possibilities of the effective applications of the discussed algorithms in different practical technical problems are showed in the paper. Research, done till now, indicate the chances of applying the proposed algorithms in certain technical problem in which the incomplete projection data appear (like, for example, in searching for the elements in material which cause decreasing of its strength or in looking for the compressed gas reservoirs in the coal bed, which can be dangerous for the people’s life and health). Originality/value: The paper presents the reconstruction algorithms (block and chaotic-bloc), designed by the authors, which appear to be more effective than the standard algebraic algorithms adapted for solving problems with the incomplete projection data.