This article describes the new model of the Universe that is an alternative for the well-known Big Bang (BB) model. The recently published paper [1], where the authors have presented data on the oldest star in the Milky Way galaxy halo, challenges the validity of the BB model claim about the age of the Universe. It is thus apparent that there is a need to develop an alternative model for the Universe that would not have this problem and provide a better agreement with observations. The model presented in this paper offers such a new alternative by assuming that the Universe is not expanding and is filled with a static gravitating "dark matter" (DM) that is transparent and therefore does not absorb light. This matter provides a framework in which the visible matter moves similarly as defects or vacancies move in a crystal floating from the bulk to the surface. It is further assumed that the visible matter may have been created from this dark transparent matter by an unspecified process sometime in the past, or is being constantly created with a smaller rate. After aggregation to stars and galaxies the visible matter is driven out to the edge of the Universe where it disintegrates and generates the immense Gamma Ray Bursts (GRB). This radiation then may contribute to the generation of new matter throughout the Universe similarly as the assumption that the matter is being constantly created in the Fred Hoyle's model of the Universe [2]. The DM model provides equations for the observed recession velocities of distant galaxies, and for many remaining parameters that follow directly from the Hubble constant such as: the size and the mass of the Universe, the maximum observable luminosity modulus, the maximum observable Z shift, the maximum galaxy recession velocity, the size of the average galaxy, etc.. An important relation, also derived from the model, is the relation between the Hubble constant and the temperature of the cosmic microwave background radiation (CMBR). This relation allows a precise calculation of Hubble constant from this temperature. The developed theory is compared with the available data of the GRBs, the Supernova Cosmology project, and the BATSE catalog, and a very good agreement is obtained.