The integral transform method (ITN) has been extended to the treatment of one-dimensional homogeneous media with linearly anisotropic scattering. A previously obtained formula linking the isotropic and the anisotropic one-dimensional kernels allows for calculation of the anisotropic matrix elements in the form of linear combinations of a few isotropic matrix elements. In practice, to solve the anisotropic problem of order N one needs only to calculate the isotropic collision matrix of order (N + 2) in plane and spherical geometries and of order (N + 1) in cylindrical geometry. The method is applied to the calculation of critical parameters for bare cylinders. Highly accurate values, to be used as benchmarks, are obtained and illustrate the precision and fast convergence rate of the method.