In order to research the static security assessment result for transmission lines considering the uncertainty of loads and Distributed Generations (DGs) output power, a Sampled-Blind-Number (SBN) based static security assessment for transmission lines is put forward. Firstly, the sampling method for the static security assessment is described, in which the SBNs of a load and the output power of a DG are calculated from the annual load duration curve and the annual output power duration curve, respectively. The scenarios for analysis are furnished from combining the corresponding SBNs of the loads and DGs output power. On this basis, whether the loading of the other transmission line or grid equipment under the N-1 assessment is over its rated value is analyzed. The probability of being against the N-1 criterion for grid is obtained as the summation of the probabilities of the scenarios which are with overloaded situations. Finally, the transmission lines with risk of being against N-1 criterion are ranked by the probability of risk to find the vulnerable spots of grid. An example is given to explain the proposed approach and the simulation result shows SBN method is feasible for N-1 static assessment and suitable for the multi-dimension evaluation for grid. This work is supported by Key Research and Development Program of Shaanxi Province (No. 2017ZDCXL-GY-02-03).