Computational mechanics routinely deals with nonlinear, multiscale, and heterogeneous problems whose numerical treatment challenges classical computing. This raises the question of whether quantum computing can provide alternative algorithmic approaches for the numerical solution of partial differential equations (PDEs) and related models, and what form such approaches could take. We address this question by presenting recent developments in quantum algorithms for computational mechanics. We emphasize algorithmic ideas that connect quantum methods with established techniques in computational mechanics, focusing on quantum versions of familiar numerical tools such as finite element methods, Newton-type solvers, and Gaussian random field generation. The presentation is complemented by numerical experiments on quantum simulators and current noisy quantum hardware, clarifying both feasibility and limitations.