Simultaneous methods for finding multiple zeros of a polynomial are considered. The proposed class of methods has a multipoint character and does not require a knowledge of the multiplicity order of the sought zeros, which is the main and favorable feature of these methods. To avoid division by zero in the case of the same approximations, the differences $z_i-z_j$ in iterative formulas use the approximation $z_i$ from the $m$th iteration and the approximations $z_j$ $(j\neq i)$ from the $(m-1)$th iteration. The convergence analysis of the most, frequently used simultaneous methods in multipoint mode is given. It is shown that the iterative methods with corrections are not efficient since their order of convergence is considerably reduced.