In the commonly used technique of scanning calorimetry, one measures the heat capacity, Cp, as a function of temperature T on heating or cooling a material at a fixed rate. In the study of liquid-glass-liquid transition, a calorimetry scan is modelled in terms of a non-exponential parameter, β, and non-linearity parameter, x, which describe the shape of the Cp-scan as well as the time- and temperature-dependence of structural dynamics. A liquid also becomes glass on isothermal pressurizing and the glass is expected to become liquid on depressurizing. Here we describe the formalism of a technique in which the volume, V, may be measured as a liquid is isothermally pressurized at a fixed rate, r = (dp/dt)T, to form glass, and also as the glass is isothermally depressurized at a fixed rate until it becomes liquid. We name it pressure scanning volumetry (PSV) and simulate the pressurizing and depressurizing scans of (dV/dp)T within the framework of non-exponential, non-linear structural relaxation. Hence we show how the features of simulated PSV scans change with change of, (i) the pressurizing and depressurizing rates, (ii) the parameters β and x, and (iii) the volume of activation for characteristic relaxation time, ΔV*. We also describe how the limiting fictive pressure, pf′, can be determined from a PSV scan, and fit the PSV formalism to the available bulk modulus against p plot of atactic poly(propylene) at 297 K [S.P. Andersson, O. Andersson, Int. J. Thermophys. 18 (1997) 845-864] to obtain β, x and ΔV*. In addition to being of academic interest, the formalism would be useful for modelling polymer extrusion processes. The study may also stimulate commercial development of equipment with computer-controlled pressure-change for use in studies of academic and technological significance.