New results obtained in experiments on laser irradiation (I = 1014 W/cm2, λ = 1.055 micrometer) of lowdensity (1–30 mg/cm3) fibrous and foam‐like materials are presented and discussed. Influence of low‐density material microstructure of irradiated plane samples on processes of laser light absorption, X‐ray conversion, energy transport, plasma formation and homogenization was investigated. The pronounced effect of material microstructure on the parameters and dynamics of produced plasma has been found out using the variety of complementary X‐ray and optical methods. The extension of hot plasma region inside irradiated samples as well as the energy transport rate was observed to be several times higher for samples of foam‐like polystyrene than for samples of fibrous agar. The experiments with cascade targets consisting of several mylar films (film thickness and film‐to‐film spacing were varied) were carried out with the aim to model the polystyrene microstructure in a simplified manner. The low‐density fibrous samples with external and internal soft X‐ray sources (converters) were also irradiated. Preferences of either fiber or foam‐like material utilization in target constructions for specific research problems are considered. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)