According to the uncertainty and the inherent randomness of unmeasured nodal positions, a stochastic deviation method (SDM) was proposed to reckon the geometric shapes of existing spatial structures. In a consideration of the characteristics of spatial structures, the sampling principle and the minimum sample size calculation approach in SDM were given. Based on the probability and the statistics theory, the procedure for inferring the random fields of nodal position deviations was built. In addition, the prior information concept was introduced into SDM, and approaches for inferring the stochastic parameters with prior information were put forward based on the Bayesian statistics theory. Finally, the proposed SDM was adopted to reckon the geometric shape of reticulated shell structures, and the nonlinear static stability analysis was carried out using SDMdetermined structural spatial positions. It is shown that SDM can give realistic results and be used for the appraisal of existing spatial structures.