The one-dimensional fluid code SOLF1D has been used for modelling of plasma transport in the Scrape-Off Layer (SOL) along magnetic field lines, both in steady state and under transient conditions that arise due to plasma turbulence. The presented work summarizes results of SOLF1D with attention given to transient parallel transport which reveals two distinct time scales due to the transport mechanisms of convection and diffusion. Time-dependent modelling combined with the effect of ballooning shows propagation of particles along the magnetic field line with Machnumber up to M 1 and supersonic transport when plasma-neutral interactions are not present. Asymmetric heat and particle fluxes are analyzed for a case with poloidally asymmetric radial outflow (ballooning) and for a radial outflow with parallel momentum (rotation). In addition, parallel damping of the density and electron temperature calculated in SOLF1D is compared with the approximative model used in the turbulence code ESEL both for steady-state and turbulent SOL. Dynamics of the parallel transport are investigated for a simple transient event simulating the propagation of particles and energy to the targets from a blob passing across the flux tube at the outboard midplane and for time-dependent data provided by ESEL.