The pressure–stress image analysis method for measuring pointwise pressures and stresses from the curvature of liquid interfaces is presented. The weak force of surface tension provides a precise relative measure for other forces, such as pressure, stress, and buoyancy. In particular, the pointwise jump in pressure or normal stress can be determined from the shape of an axisymmetric liquid interface. The resulting stress profile is a more direct measure of the forces on a liquid surface than global measures such as Bond number. In the static case, the jump in normal stress is the pressure jump at the capillary surface. Pointwise precisions of better than 0.01 Pa in pressure are readily attainable for static systems. In such systems, the pressure profile gives the force of surface tension relative to gravity, reproducing the classical method of measuring surface tension from pendent and sessile drop shapes. In flow systems, the stress profile provides information about local flow effects. An application for balancing gravity effects with axial flow is provided as a practical example.