The conceptual design of a neutron source is described. This device, called Very Intense Neutron Source (VINS) would produce bursts of neutrons to be used for fast- and thermal-neutron beam experiments by time-of-flight methods. The source would have an effective source flux for beam experiments several orders of magnitude above those fluxes now available at the best neutron sources. In the concept, the neutrons produced by an electron linear accelerator would be multiplied by fast reactor modules. These modules would be arranged to provide maximum multiplication while limiting the shock and heat and limiting multiplication of those neutrons from the delayed-neutron precursors. The experimental arrangement and uses of VINS are stressed.