The two-dimensional problem of convective diffusion of ions near a small electrode is solved by using die boundary integral method. Ion concentration at the wall is expressed as a convolution of the electrode current density and the Green function, which is obtained in Fourier space for a linear velocity profile in terms of the Stokes function. Current density distributions for a strip-shaped electrochemical probe are calculated numerically from an integral equation derived from the boundary condition, The frequency response of the probe is investigated by the method of imposed small shear stress harmonic oscillations, The finite electrode reaction rate is taken into account, As a result, the steady state current and linearized frequency response of the probe are calculated for a wide range of Peclet numbers and applied voltages.