Stochastic velocity fields with finite correlation lengths affect the formation of interstellar (intergalactic) absorption lines in a way not accounted for in the standard analysis procedure in which Voigt profiles are fitted to the observed line profiles, We investigate these effects, accounting in particular for the fact that interstellar absorption spectra reflect only one realization of the velocity held. since (i) actually only one line of sight is observed and (ii) the velocity structure of the cloud has to be considered to be 'frozen' over the exposure time. This paper presents results of Monte Carlo calculations, In this technique an ensemble of line profiles is computed, each one of which corresponds to one realization of the random velocity field, The most important results are the following, (1) The individual line profiles may deviate substantially from each other and from the ensemble average, (2) Correlated velocity fields may cause complex multicomponent absorption features which in a traditional analysis would be attributed to several clouds, i.e. to density and/or kinetic temperature inhomogeneities. (3) Each lint of sight has its own curve-of-growth, (4) Applying the standard analysis to such line profiles may produce misleading results concerning the physical parameters of the cloud. (5) In particular, the apparent scatter of the D/H ratio revealed in the ISM on the basis of the Copernicus, IUE, and HST observations may be caused by an inadequate analysis. Finally, we discuss under which conditions cloud characteristics may be derived from absorption lines without relying on a particular physical model.