Characterizing dynamic characteristics of structures with uncertainty is an important task that provides critical predictive information for structural design, assessment, and control. In practical applications, sampling is the fundamental approach to uncertainty analysis but has to be conducted under various constraints. To address the frequently encountered data scarcity issue, in the present paper Gaussian processes are employed to predict and quantify structural dynamic responses, especially responses under uncertainty. A self-contained description of Gaussian processes is presented within the Bayesian framework with implementation details, and then a series of case studies are carried out using a cyclically symmetric structure that is highly sensitive to uncertainties. Structural frequency responses are predicted with data sparsely sampled within the full frequency range. Based on the inferred credible intervals, a measure is defined to quantify the potential risk of response maxima. Gaussian process emulation is proposed for Monte Carlo uncertainty analysis to reduce data acquisition costs. It is shown that Gaussian processes can be an efficient data-based tool for analyzing structural dynamic responses in the presence of uncertainty. Meanwhile, some technical challenges in the implementation of Gaussian processes are discussed.