In both the analysis and appraisal of existing spatial structures，structures should be modeled in accordance with the actual geometric shapes. A function of correlation coefficient was recommended to model the correlated deviation of nodal positions according to the geometric characteristics of the existing spatial structures, and the approach to calculating model parameters was given. Based on the correlation analysis of nodal positional deviations，a new method of reckoning the structural geometric shapes by sampling nodal positions was proposed. In the proposed method, the deviation distributions of unmeasured nodal positions can be inferred from sampling data where expectations should be calculated by conditional distributions and variances would be estimated as upper limits of the confidence intervals from the cross validation. Then, using the calculated deviation distributions, uncertain geometric models can be established to analyze and assess the existing spatial structures. Through calculating the shell shape by sampling the nodes and analyzing its overall stability, it concludes that the method based on nodal positions correlation analysis meets the actual case. The proposed method was applied to reckoning the geometric shape of a reticulated shell structure，and the nonlinear static stability analysis was carried out. It is shown that the proposed method can give reliable results and apply to the appraisal of existing spatial structures.