The extension of the European Union with the last two “waves† of new members in 2004 and later in 2007 brought new opportunities for the countries in Eastern Europe, especially those linked with the usage of European funding to support public or private investments. It is obvious that “effective utilisation of EU support can foster the success of economic performance†(European Commission, 2009). Financing investment projects proposed by the SMEs can be realized through several financial programmes, especially those established under the European Regional Development Fund (ERDF). In order to be approved investment projects must comply with the requirements of the financing program especially those related to a proper realized Cost Benefit Analysis (CBA). A major emphasis within the CBA consists from sensitivity and risk assessment modelling. Sensitivity analysis aims to identify those variables / risks that may impact during project development and operational period and may lead to failure of positive factors leading to significant change in the financial and economic profitability of the project. Sensitivity analysis used to measure consider identifying risk factors that have the greatest influence on the net present value in general, and in particular on EU-funded projects, the financial and economic rates from financial modelling to analyse cost-benefit analysis (CBA) (including rate gap financing for investment projects where required) and indicate their impact during project cycle reg. Sensitivity analysis can help identify poor design choices and can highlight the need to obtain further information on certain variables (European Commission, 2008). Regarding this, the current paper has as its main objectives the analysis of the decision system for approving an EU funded project. The secondary objective is to analyze the proposed indicators within the sensitivity and risk assessment system which are used for selection of investment projects. The analysis is made using as a case study an investment project developed by Romanian companies. Both approaches of sensitivity analysis: deterministic and stochastic analysis, were tackled within the paper. As final conclusions of this paper we will demonstrate the theoretical and practical role of cost-benefit analysis – sensitivity and risk assessment to select the best applications that will be proposed for funding under the European grant programs.