We aim to study the formation and evolution of solar spicules by means of numerical simulations of the solar atmosphere . With the use of newly developed JOANNA code , we numerically solve two-fluid ( for ions + electrons and neutrals ) equations in 2D Cartesian geometry . We follow the evolution of a spicule triggered by the time-dependent signal in ion and neutral components of gas pressure launched in the upper chromosphere . We use the potential magnetic field , which evolves self-consistently , but mainly plays a passive role in the dynamics . Our numerical results reveal that the signal is steepened into a shock that propagates upward into the corona . The chromospheric cold and dense plasma lags behind this shock and rises into the corona with a mean speed of 20-25 km s ^ { -1 } . The formed spicule exhibits the upflow/downfall of plasma during its total lifetime of around 3-4 minutes , and it follows the typical characteristics of a classical spicule , which is modeled by magnetohydrodynamics . The simulated spicule consists of a dense and cold core that is dominated by neutrals . The general dynamics of ion and neutral spicules are very similar to each other . Minor differences in those dynamics result in different widths of both spicules with increasing rarefaction of the ion spicule in time .