Electromagnetic properties of the superconductors predestine them to serve as materials for the efficient and light magnetic shields. Very high attenuation factors are possible to be obtained. Superconducting elements of different geometry can be used. However, shielding effect is limited by the critical current of a superconductor. This work describes the model of an arbitrarily shaped thin superconducting plates made of BSCCO, with the focus on circular and rectangular samples. The plates are subjected to transverse magnetic fields of different strength and shape. Changes of critical current density are considered. The distribution of the shielded magnetic field and shielding current is presented. Results show that the magnetic field attenuation occurs and depend on the shape and material of a plate. It was also observed that coarse meshes can be used to obtain reliable results concerning magnetic field distribution, thus saving computational time.