The cross sections for fissioning of 235'238U by fast neutrons have been studied experimentally in greater detail and with higher accuracy than the same cross sections for other actinide nuclei. As a result, they are used as neutron standards in the range of neutron energies E n from several hundreds of keV up to 20 MeV [1]. They are widely employed in relative measurements of other cross sections, primarily the fission cross sections of less-studied nuclei. This methodological solution considerably expanded the possibilities for performing systematic investigations of af(E n, Z, A) for many nuclei that play an appreciable role in nuclear technology. However, the requirements of nuclear technology cannot be solved by measurements alone, especially in the case of highly active short-lived target nuclei. Attempts are being made to eliminate the associated deficiencies and problems in the experimental information by means of theoretical calculations [2][3][4][5].For a long time the capabilities of theory fall far short of the practical requirements. This unbalance has been greatly reduced. In the present paper we calculate the fast-neutron fission cross sections of 235'238U by the approach developed in [5, 6], which has made possible the greatest advance toward a systematic theoretical description. The most accurate fission cross sections are the best object for testing and estimating the accuracy of this approach. In the present paper this problem is solved by extending the calculations up to 40 MeV. The new range is two times wider than the section E n < 18-20 MeV, where the cross section trr(E n) for 235'238U target nuclei became neutron standards and analysis was performed in the preceding works [2,[4][5][6]. Basic Properties of af(En). The main feature of the fission process in the range of neutron energies E n where af(En) is to be calculated is the possibility of emission of several prefission neutrons by the excited fissioning nucleus, i.e., several (n, xn't) reactions with different number x of such neutrons or, as is sometimes said, fission chances, occur simultaneously. The observed cross section of such a process, often called emission fission, is the sumx=0 where afx(En) is the cross section for separate fission chances and Xmax(En) is determined by the threshold of (n, xn'f) reactions (in the E n scale)X--I e,= = + a , i=0and Xma x remains constant for En.x" < g n < E,tx..x + 1 (2) and increases abruptly by one unit when the upper limit determined by the formula (2) is crossed. A distinguishing property of actinides is the weak energy dependence of af0(En) and, consequently, trfx(En) is of a higher order, as a result of which Eq. (1) acquires a "stepped" character with "plateaus" in crf(En), whose width is determined from Eq. (2). What has been said above is strictly speaking true if the interaction of the neutrons with the nuclei proceeds via the formation of a compound nucleus (equilibrium mechanism), and neutron emission from the compound nucleus is described by the evaporation model. These prope...