A method for the production of a cross-linked support matrix that in form of a bed will permit liquid flow velocities above 5 cm/h, preferably above 50 cm/h, to pass through the bed. The method is characterized in that it comprises the steps: (a) providing a starting support matrix that has pendent unsaturated groups, and (b) subjecting said starting support matrix to electron beam or gamma-ray irradiation. The use of a cross-linked support matrix produced by a method comprising the steps of: (a) providing a starting support matrix that has pendent unsaturated groups, and (b) subjecting said starting support matrix to electron beam or gamma-ray irradiation as a support matrix in liquid chromatography, cell culturing, step-wise solid phase synthesis of organic compounds, running catalytic reactions by the use of a solid phase bound catalyst.