This is the first in a sequence of Data Items to accompany the VGK method for two-dimensional aerofoil sections. VGK is a CFD (computational fluid dynamics) method coded in Fortran for predicting the aerodynamic characteristics of a two-dimensional single-element aerofoils in a subsonic freestream, including the effects of viscosity (boundary layers and wake) and shock waves. VGK uses an iterative approach to solve coupled finite-difference equations for the inviscid flow region (assumed to be potential) and the viscous flow region (represented by integral equations). The aerofoil boundary-layers must be attached for VGK to produce results that correspond to the real flow. VGK was developed over a period of years at RAE (now DERA, Farnborough) and is made available by ESDU International plc under the terms of an agreement with DERA. Crown copyright is retained in the VGK source code. This Item describes the main features of the VGK method, including the inviscid and viscous flow elements, the computational grids, and the solution process. The precise forms of finite-difference scheme and iteration procedure employed in a particular VGK 'run' are governed by a number of parameters. The values of these parameters may be selected by the user. Default values for these parameters are given, together with comments on the effects on VGK results of variations from these values. The performance of VGK, in terms of the accuracy of its results, is considered both for inviscid flows, where comparisons with other theoretical methods are given, and for viscous flows, where comparisons with experiment are presented. For flows where the aerofoil boundary layer is attached and any shock waves present are relatively weak (which thus include most aerofoil design conditions) the performance of VGK is good, with drag coefficient being well predicted. Where the boundary layer is locally separated or close to separation, VGK can still give a valuable indication of the flow parameters, but its accuracy is then not as good. Because of its good performance, VGK can be utilised effectively to investigate a number of factors, such as: the influence of aerofoil geometry (profile and camber) changes on aerofoil characteristics at and around cruise conditions; the influence of changes in Mach number, Reynolds number and transition locations on aerofoil characteristics; the influence of deflection through small angles of leading- and/or trailing-edge flaps; the influence of over-fixing transition in wind-tunnel tests on aerofoils.