Engineering dynamical systems, such as structures subjected to time-dependent loads and mechanical vibrations, are inherently affected by uncertainties arising from material heterogeneity and stochastic external excitations, which can significantly influence system responses. Quantifying these uncertainties is therefore essential for robust design and safety assessment. A common approach to uncertainty quantification (UQ) relies on repeated simulations combined with Monte Carlo (MC) sampling. However, the high computational cost associated with large-scale models with many degrees of freedom (DOFs) renders such approaches impractical, motivating the use of surrogate models trained on a limited number of simulations to enable efficient UQ. Gaussian processes (GPs) provide a probabilistic surrogate modeling framework well suited for UQ, as they predict both mean responses and associated uncertainties. However, their cubic computational complexity with respect to the number of training samples severely limits their application to large-scale problems. In this work, we propose a reduced-order UQ framework combining Canonical Polyadic (CP) tensor decomposition and Gaussian process regression (GPR). First, high-dimensional input parameter fields (e.g. random Young's Modulus field) and output mechanical responses (e.g. element stress) are compressed into low-dimensional feature spaces (matrices) using CP. Next, apply GPR on the reduced data, enabling efficient feature-to-feature prediction. This strategy reduces the dimensionality of the learning problem from millions to hundreds of variables and improves computational efficiency. We apply our framework to two separate examples of beam under static load and plate under dynamic load conditions where material parameters (Young’s modulus, Poisson’s ratio, and density) and external loads (reproducible band-limited random signals) are random inputs. Finite element method (FEM) simulations are employed to generate training data for the framework. Numerical results demonstrate that the proposed framework substantially accelerates GP-based UQ while maintaining acceptable reconstruction and prediction accuracy.