The impact of uncertainty on the flexural response of sandwich beams is studied in this paper. The study focuses on the unique features of typical soft-core sandwich beams, including local effects and stresses concentrations. Those are critical for the integrity and performance of the structural system and, to the best knowledge of the authors, were never considered from a stochastic viewpoint. Several structural features of the beam are considered, separately, as uncertain, and the stochastic characteristics of the distributions of the displacements and stresses are investigated. To capture the unique local effects, the extended high-order sandwich panel theory is adopted. Numerical solutions of the stochastic ordinary differential equations use the finite element (FE) method. The parametric uncertainty and its spatial distribution are modeled by random fields. The stochastic analysis uses both the Karhunen–Loeve polynomial-chaos and the perturbation-based stochastic finite element methods. The two approaches are compared and comprehensively validated against Monte Carlo simulations. The numerical results quantify the impact of uncertainty on the response, but show significant disagreements between the two stochastic approaches, and the perturbation-based stochastic finite element method is chosen as the most suitable one. The effects of the coefficient of variation of the uncertain input parameter and its correlation length are also studied. Highly amplified levels of uncertainty are revealed by the stochastic analysis near points of local stress concentration. These localized yet significant uncertainties, reported here for the first time, shed new light on the design, analysis, and safety of such sandwich beams.