It is practically difficult to collect sufficient probability information for structural random variables. Moreover， actual dynamic loads also increase the difficulty in probability-based reliability evaluation. Therefore， dynamic loads are first simplified into quasi-static loads. Then a new concept of quasi-static deflection surface has been proposed based on the concepts of quasi-static deflection curves and displacement influence lines commonly-used in the civil engineering realm. The mathematical expressions of deflection surfaces are then deduced using the principle of virtual work. Uncertainties in the geometrical dimensions， material properties and external loads of a structure are reflected by interval variables， by which means a quasi-static deflection surface is extended to a quasi-static deflection interval enveloping surface. After that， an experimental simply supported steel box beam has been taken as an example for validation. A quasi-static interval reliability index is proposed according to the relationship between the measured deflection surface of the beam and its deflection interval enveloping surface. The reliability of the beam before and after damage can be evaluated using the interval reliability index. The analysis results demonstrate that the uncertainties in both structural parameters and loads can be effectively considered in the quasi-static deflection interval enveloping surface， and the interval reliability index decreases with the damage severity increase of the beam.