The paper is a review work devoted to dished heads of various meridian shapes. Geometry of the shells of revolution, the membrane state, and the edge effect occurring in the shells are described. Exemplary analytical and numerical finite element method (FEM) studies of torispherical, ellipsoidal, Cassini-ovaloidal, and untypical special dished heads are presented. The results of the above-mentioned two methods are compared. Moreover, numerical research of elastic buckling of the above-mentioned selected heads under external pressure is carried out. Literature related to each of the considered head types is quoted and discussed, with special attention paid to the works developed in the 21st century. In concluding remarks, the stress concentration and buckling of these structures are commented, with consideration of the head meridian shapes.

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