The problem of elastic stability herein for payload aerodynamic fairing of a composite material with discrete longitudinal connections loaded under external excessive pressure is presented. The calculation of parameters of critical external pressure was performed by method of finite element. The forms of loss of stability and values of critical load were determined as a result of calculations for various cases of loading and various parameters of longitudinal joint. The estimation of influence of parameters of the longitudinal joint (number of discrete links, stiffness of the longitudinal beams) on the critical external pressure value was carried out.