Density distribution in the (r, z)-plane in the domain r ∈  [0,r_max] , z ∈  [0,L/2]  for prominence thread models with non-uniform radial and longitudinal structuring. The threads are defined by a cool and dense part with density, ρ_f and length L_thread and an evacuated part of the tube with density ρ_ev and length L − L_thread. These two regions connect non-uniformly to the coronal surrounding medium with density ρ_c. Depending on the value of ρ_ev, three different situations are possible: a) ρ_ev = ρ_c; b) ρ_c ≤ ρ_ev ≤ ρ_f; and c) ρ_ev ≤ ρ_c.