The paper deals with supersonic flows around. blunt bodies with bielliptical cross sections. The family of bodies includes as special cases a circular cone and an elliptical delta wing with spherical noses. To compute the flows the well-known method of Babeako-Voskre-seaskiy is used with some modifications for more succesful application. Numerical results are given to show possibilities of this modified version of the method. Some gasdynamic effects are discussed which appear in the flows in consequence of angle of attack or slip angle. One of these effects, for instance, consists in that “the locality” of the flows about leeward and windward surfaces of a given body is more noticeable that one would expect it to be judging by the form of the cross section.