Accurate prediction of remaining useful life (RUL) will improve reliability and reduce maintenance cost. Therefore, prognostics is essential to predict the RUL of systems and components. However, a big issue of uncertainty prevails in prognostics due to the fact that prognostics pertains to prediction of future state, which is affected by uncertainty. While various researches have been done in areas of prognostics and health management, they lack to perform RUL predictions efficiently. There is a need for an efficient comprehensive framework for quantifying uncertainty in prognostics. The research question to this study is: can meshfree modeling be used in probabilistic prognostics to efficiently predict RUL? The specific aims developed to answer the research question are (1) develop a computational framework for probabilistic prognostics of a fatigue life of a component using meshfree modeling, and (2) perform case study analyses on fatigue life of a cantilever beam. A probabilistic framework was developed that efficiently predicts the RUL of a component using a combination of the meshfree method known as local radial point interpolation method and a fatigue degradation model. Loading uncertainty is quantified and employed in the framework. The computational framework is easily customizable and computationally efficient and, hence, aids in decision making and fault mitigation. As a case study, the RUL of a cantilever beam under plane stress subjected to fatigue loadings was analyzed. Uncertainties in the RUL were quantified in terms of probability density functions, cumulative distribution functions, and 98% bounds of confidence interval. Sensitivity analysis was studied and computational efficiency of the framework was also investigated using first order reliability method and Monte Carlo method. When compared to the Monte Carlo method, first order reliability method provides reasonably good results and is found to be computationally more efficient.