In accordance with demands of the National Program for Medium- and Long-term Scientific and Technological Development for cutting-edge research on hydro-structure engineering, and in consideration of the characteristics of high dams, super high dams, and dangerous dams, significant scientific and technological problems in hydro-structure engineering are examined. Representative achievements and progress in research on stress, ultimate bearing capacity, and nonlinearity analysis are reviewed, and then the advantages and disadvantages of current theories and methodologies are analyzed. Finally, development directions, including the macro-meso-nano coupling analysis model, micro-nano scale analysis method, stochastic fatigue theory, and the comprehensive analysis theory and method for health diagnosis based on stress, ultimate bearing capacity, and nonlinearity analyses in hydro-structure engineering, are proposed.