Solid stress and tissue stiffness affect tumour growth, invasion, metastasis and treatment. Unlike stiffness, which can be precisely mapped in tumours, the measurement of solid stresses is challenging. Here, we show that two-dimensional spatial mappings of solid stress and the resulting elastic energy in excised or in situ tumours with arbitrary shapes and wide size ranges can be obtained via three distinct and quantitative techniques that rely on the measurement of tissue displacement after disruption of the confining structures. Application of these methods in models of primary tumours and metastasis revealed that: (i) solid stress depends on both cancer cells and their microenvironment; (ii) solid stress increases with tumour size; and (iii) mechanical confinement by the surrounding tissue significantly contributes to intratumoural solid stress. Further study of the genesis and consequences of solid stress, facilitated by the engineering principles presented here, may lead to significant discoveries and new therapies.