There are various factors in the analysis and design of steel frames that uncertainty of them can have a significant effect on the structural safety. Accordingly, study of these factors to understand the actual behavior of the structure are important. Meanwhile, the initial stiffness of beam-to-column connection, can be considered as one of these variable. Therefore, in this paper, the effects of uncertainty in the initial stiffness of BUEEP, WFP and BSEEP connections, from rigid connections pre-qualified of Iran steel codes, on drift of simple steel frame are evaluated. In the firstly, the initial stiffness of mentioned connections based on the mechanical method of the European Code (EC3) and numerical method based on the finite element method by using of the commercial software ABAQUS obtained. By evaluating the responses of the two methods with experimental findings, stiffness obtained from finite element method selected as appropriate stiffness. Then, the probabilistic analysis performed by using of the Monte Carlo simulation method. It should be added, for stiffness of any connections, uniform distribution , normal distribution and lognormal distribution with coefficient of variation from 5 up to 20 percent are considered and drift of frames for thousands simulation are calculated. Results that exceed the allowable drift of Iran code, indicating count of failure of structure. Accordingly, the structure analysis performed 72000 times and probability of the failure will be evaluated. For all connections, the probability of failure for different distributions and coefficients of variation graphically displayed. In the following, reliability of the frame obtained from graphs of cumulative distribution function (CDF). Moreover, for any of the connections and in all investigated cases, a reduction coefficient to achieve 100% reliability and coordination of lateral displacement of with allowable drift with Iran codes becomes available.