Knowledge about strain at the nanometre scale is essential for tailoring the mechanical and electronic properties of materials. Flaws, cracks and their local strain fields can be detrimental to the structural integrity of many solids(1,2). Conversely, the controlled straining of silicon can be used to improve the performance of electronic devices(3-5). Here, we demonstrate that infrared near-field microscopy(6) allows direct, non-invasive mapping and a semiquantitative analysis of residual strain fields in polar semiconductor crystals with nanometre-scale resolution. Our experiments with silicon carbide crystals yield optical images of nanoindents showing strain features as small as 50 nm and the evolution of nanocracks. In addition, by imaging nanoindents in doped silicon, we provide experimental evidence for plasmon-assisted near-field imaging of free-carrier properties in nanoscale strain fields. Near-field infrared strain mapping provides possibilities for nanoscale material and device characterization, and could become a tool for nanoscale mapping of the local free-carrier mobility in strain-engineered semiconductors.