Scientists and concrete technologists have been working on the development of new types of concrete. Newly elaborated material provides improved mechanical and physical properties. The deformation characteristics of concrete are important in the design of sustainable structures [1]. This paper introduces the recent state of research on elastic and time-dependent deformations of new high performance cement composite materials (FRCC) that are reinforced with polyvinyl alcohol (PVA) fibres and sub ected to long-term, uniform, constant compressive load. In these composites, part of the cement has been replaced with micro- and nano-fillers. The experimental studies of creep in compression were performed. The concrete specimens were tested in a controlled constant temperature and with a constant level of moisture. This study was carried out on two different extreme cases of environment: the case with 100% moisture of specimens obtained by protecting to desiccation of this one and the case of air-dried specimens. Specimens were tested at age of 28 days. The compression strength and modulus of elasticity of HPFRC concrete specimens were determined. The results of the experiments permit the prediction of long-term deformations of the concrete.