This paper presents a stochastic analysis of expressions linking the reinforced concrete (RC) buildings maximum displacements to their natural period and the epicentral distances. Where, low- and medium-rise reinforced concrete buildings, are tested under the effect of records collected during the Boumerdes earthquake (Algeria, May 21st, 2003) at different epicentral distances. First, the expressions linking building maximum displacement and interstory drift to the building natural period and epicentral distance are derived. Then, using Monte Carlo simulation, the effect of the uncertainty of the chosen parameters on the confidence intervals of the lateral displacement and interstory drift statistics is studied, where the natural period and the epicentral distance are considered as random variables with a log-normal distribution. The findings denote that the derived expressions are less influenced by fundamental period uncertainty than the that of the epicentral distance. A good accuracy in the established formulations is reflected by the small width of the confidence intervals of the both analyzed responses.