A method is described for computing, from first principles, the diffraction pattern from an array of parallel slits in a thin perfectly conducting screen. The incident wave is plane and has an arbitrary direction. Babinet's principle relates this problem to that of the complementary screen, an array of parallel strips. It is already known that the whole problem may be reduced to the solution of two integral equations. Two suitable ones are derived and solved numerically for the case of one or two strips or slits; the extension to more than two is then obvious. The interaction between the strips is clearly seen in the distributions of surface currents induced in them; these are shown graphically for different polarizations, widths and angles of incidence. The field distributions very near to the screen are presented as contour maps and compared with microwave measurements made by the modulated scatterer method; the far field is also examined. For wide strips or slits an alternative approximate numerical method is suggested.