Wigner sampling (WS) combined with classical molecular dynamics is a powerful combination for describing nuclear quantum effects and vibrational anharmonicity at a reasonable computational cost. In this work we briefly describe the underlying theory and introduce a new procedure, denoted as simplified Wigner sampling (SWS). In contrast to WS, this procedure does not require initial calculation of Hessian. Instead, it can be controlled by a single parameter τ , whose optimal values can be found in the interval 1 ≤ τ ≤ 10 fs.