Abstract: Aiming at the static stability of the parabolic single-layer cylindrical reticulated shell， the following research is conducted: the static stability of the parabolic single-layer cylindrical reticulated shell is compared with that of the single-layer cylindrical reticulated shell and the inverted catenary single-layer cylindrical reticulated shell. A large scale parameter analysis is carried out on the parabolic cylindrical reticulated shell. An optimized design for the parabolic single-layer cylindrical reticulated shell is conducted. Research shows that compared with the cylindrical reticulated shell， the ultimate load of the parabolic single-layer reticulated cylindrical shell is greatly enhanced. Rise-span ratio and length-span ratio influence the ultimate load of the shell significantly. The shell is proved to be sensitive to initial geometric imperfection. There exists an optimal oblique rod intersection angle of about 50° under which the static stability is the best. When the grid space layout is arranged according to the geometric series and the value of the ratio α is between 0.85 and 0.95， the static stability of the shell is the best.

Key words: single-layer reticulated cylindrical shell, cylindrical, parabolic, inverted catenary, ultimate load