Slender shell structures described by ruled surfaces have been frequently used in civil engineering due to the fact that they are one of the most economical structural solutions to cover large spans. Ruled surfaces are obtained by the movement of one or more lines along one or more curves. So they are easy to cast, which justifies their choice in many cases. For aesthetic and structural reasons these structures are usually shallow surfaces, which leads, as in the case of shallow arches, to a strong geometric nonlinearity. Among the shells described by ruled surfaces, conoidal shells are frequently favored as roofing units to cover large column-free areas due to the ease of fabrication, aesthetic elegance and good provision of natural light. A conoidal shell is a special case of cylindroids belonging to Catalan’s surfaces and is generated by a variable straight line moving parallel to a plane, known as the director plane, with one of its ends on a plane curve and the other on a straight line. Sometimes a part of the conoidal surface at the straight end is cut off giving a truncated configuration. The objective of this work is to analyze, using a finite element formulation, the buckling and vibration characteristics of this structural form. A detailed parametric analysis is conducted to understand the influence of boundary conditions, different spans, widths, and other physical dimensions on the static and dynamic characteristics of the structure. Specific conclusions are drawn at the end, to summarize the contributions of the present investigation, which are expected to serve as important design aids to engineers engaged in shell construction.