The magnetic and transport characteristics of a polycrystalline superconductor are investigated theoretically starting from the results on the energy distribution of an Abrikosov vortex in the vortex-laminar model [L. V. Belentsov, Low Temp. Phys. 31, 116 (2005)]. It is shown that these properties depend largely on the normalized grain size, the intergrain coupling strength, the anisotropy, and the degree of surface smoothness (“specularity”) of the material. The first vortex entry field Hp, the first critical field Hc1, and the Gibbs free energy are calculated, and also the field dependence of the magnetization M(H), pinning potential Up(H), and critical current density Jc(H) near H∼Hc1. The vortex-vortex interaction energy is found.