An exact solution of Einstein's vacuum equations representing uniformly accelerated particles was given by Bonnor & Swaminarayan. The radiative properties of this solution are here investigated by Bondi's method. After the introduction of the metric due to Bondi, the news function is found and the asymptotic behaviour of the Riemann tensor is analysed. The non-vanishing news function and the radiative character of the Riemann tensor at light infinity indicate that the solution is of radiative type: in particular, the solution is radiative in the case of freely gravitating masses. By comparing the solution of Bonnor & Swaminarayan with Born's solution in electrodynamics the results of Bondi's method are modified for the system which is not permanently isolated. The angular distribution of the radiated energy and the total rate of radiation of energy and momentum are found in the case of freely moving particles with sufficiently small masses. Gravitational radiation of the particles in question is very similar to electromagnetic radiation of an analogous system of charges. At the moment when the masses or the charges are at rest, the resulting expressions are corroborated on the basis of the approximation method of Bonnor & Rotenberg and of the standard multipole expansion method. The radiation has octupole character. In addition to outgoing radiation, incoming radiation with similar properties is present. This incoming radiation can exist in spite of the radiation condition; an additional condition which excludes the incoming radiation is suggested.