Using the large acceptance Time Projection Chamber of experiment E895 at Brookhaven, measurements of collective sideward flow in Au+Au collisions at beam energies of 2A, 4A, 6A, and 8A GeV are presented in the form of in-plane transverse momentum <p(x)> and the first Fourier coefficient of azimuthal anisotropy v(1). These measurements indicate a smooth variation of sideward flow as a function of beam energy. The data are compared with four nuclear transport models which have an orientation towards this energy range. All four exhibit some qualitative trends similar to those found in the data, although none show a consistent pattern of agreement within experimental uncertainties.