Smith-Purcell radiation (SPR) is emitted when a charge passes above a periodic grating. It is characterized by a broad range of wavelengths in which the wavelength depends on the angle of observation. Terahertz generation and non-destructive bunch length diagnostics of relativistic electrons are possible applications of SPR. Especially in the highly relativistic regime mathematical boundary condition assumptions such as infinitely long or infinitely wide grating can become inaccurate. Rigorous model for SPR calculation by the electric-field integral equation method for a grating of finite width and length is presented.