Until now, it has been impossible to visualize and quantify the finite strains and rotation components of deformation in flowing fluids by other than numerical methods. A new practical method is presented for studying both the displacement and deformation of fluid volumes in low inertia flows from physical laboratory experiments. The philosophy behind the method is outlined, and its potential is concisely illustrated with some preliminary results. These consider the finite deformation of fluid volumes creeping past a falling cylinder (Re=3¿10-9) and through a thermal convection cell with axial symmetry (Ra=104, Pr=108). Their respective deformation fields have been summarized in contour maps of the finite strain intensity, finite strain ellipsoid shapes, and their finite rotation angles. Laboratory studies of progressive finite deformation of fluid volumes in low inertia flows are of particular interest to geophysics and structural geology, but might also open new avenues for other disciplines. ¿ American Geophysical Union 1988