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Sputtering by ions with low near-threshold energies is investigated. Experiments and simulations are conducted for tungsten sputtering by low-energy, 85-200 eV Ar atoms. The angular distributions of sputtered particles are measured. A new method for molecular dynamics simulation of sputtering taking into account random crystallographic surface orientation is developed, and applied for the case under consideration. The simulations approximate experimental results well. At low energies the distributions acquire "butterfly-like" shape with lower sputtering yields for close to normal angles comparing to the cosine distribution. The energy distributions of sputtered particles were simulated. The Thompson distribution remains valid down to near-threshold 85 eV case. Highlights Angular and energy distributions of sputtered particles are considered for low-energy sputtering. A new algorithm for molecular dynamics simulations of polycrystalline target is proposed. Results of the simulations agree with experimental findings both obtained by us and found in literature.