Abstract <p>We study the propagation of soft X-rays in conical hollow through nano- and micropores of polymer track membranes. The distribution of the field amplitude and the transmission coefficient of the conical structures are determined. The problem is of interest for two reasons. First, the conical shape of pores in track membranes is the norm rather than an exception to the rule. It is determined by the final ratio of the etching rates of the intact polymer and the membrane material in the track region. Secondly, the concentration of soft X-rays at the output from the conical pores of the sample has been scarcely studied. Calculations are performed for porous membranes made of polyethylene terephthalate at wavelengths of 13.3 and 30.4 nm at normal incidence of radiation on the pore end and at various angles of the pore cone. Examples of calculations for oblique incidence of radiation on the sample are presented, and the effect of the damaged pore wall layer on the calculation results is discussed.</p>