<p>In structural engineering, the reliability and performance of structural elements under variable conditions are crucial. This paper addresses the stochastic analysis of the simple but important problem of beam deflection under off-center point load, considering variability in the modulus of elasticity due to material variations, manufacturing processes, and environmental factors. This work introduces explicit analytical formulae for the beam deflection due to off-center point load in case of random/uncertain modulus of elasticity that can be directly used by designers without need to re-computing the random effects. The Gaussian and non-Gaussian effects due to variability of modulus of elasticity are estimated and compared. Using Polynomial Chaos Expansion (PCE) and Monte Carlo (MC) simulations, we quantify uncertainty and analyze its impact on beam deflection. PCE represents stochastic processes with orthogonal polynomials, efficiently capturing random input effects, while MC simulations estimate statistical properties through numerous random samples. The mean and variance of the beam deflection are calculated at different locations of point load and compared in all cases. It was found that randomness in material properties weakens the structural elements and hence increases the deflection. The relations of deflections are deduced for different load locations and different variation in material properties. This study highlights the strengths and limitations of PCE and MC, offering insights for improved design guidelines and standards in structural engineering.</p>