The article is concerned with the methodology of economic substantiation of real investments in case of considerable lack of information on possible fluctuations of initial parameters and the resulting risk. The analysis of sensitivity as the main instrument for accounting the risk in the indicated problem situation is the focus of the presented research. In the publication, on the basis of the apparatus of interval mathematics, a set of models for comparative estimation of economic attractiveness (efficiency) of alternative investment projects in conditions of uncertainty and risk is formulated, using the sensitivity analysis. The developed instrumentarium assumes both mono- and poly-interval version of the sensitivity analysis. As the risk component in the constructed models is used: in some – values of the specially developed sensitivity coefficient, in others – the worst values, which are based on the interval estimations of the partial criteria of efficiency. The sensitivity coefficient, according to the approach proposed in the publication, is the ratio of the target semi-range of variation to the increase (economy) of efficiency, which is provided when the basic level of the analyzed partial criterion of economic attractiveness in comparison with some of its threshold (limit) value is being reached.