The bolt slippage of gusset joints can cause structural deformation in aluminum alloy single-layer reticulated shells. The magnitude of deformation depends on the axial displacement of gusset joints, thus, a reasonable axial stiffness of gusset joints can model the bolt slippage to calculate the structural deformation. A stochastic-polylines model is proposed for the distance of bolt slippage influenced by the random error of bolt geometries. It is found that the structural deflection calculated with the stochastic-polylines model can be fitted by that calculated with an ideal four-polylines model. Based on the four-polylines model, a case study is used to research on the structural deflection which varies with bolt pre-tightening force. It is found that if pre-tightening forces are larger than a limit value, the structural deflection ranges with a small amplitude, otherwise it increases distinctly. Further numerical analysis concludes that the maximum deflection approximately linearly varies with the number of grid rings and the gap between bolt and hole. And it is also affected distinctly by the structural span, the ratio of structural height to span and support type, but uncorrelated with the geometry of member section and joint gusset and the scale of loads. Then, a formula to compute the maximum deflection is proposed. And the optimum diameters of holes in gusset joint are lastly suggested for the widely used bolt and rivet connections.