For a metal deposition problem with a stagnant binary electrolyte a study is made of how low amplitude irregularities in the electrode surfaces evolve with time. The linear stability problem is solved numerically as an eigenvalue problem. Analytical solutions for three different limits are obtained and found to agree with the numerical solution. In contrast to previous work simultaneous perturbations to both electrodes are treated and the full equation for the electric potential is solved. Also, the common assumption of neglecting the time derivative in the equation for concentration perturbation is not made use of. As a result, the growth rate for very large wavelengths is found to approach a finite value rather than decreasing to zero. Non-dimensional parameters are identified and their influence is studied. As in most previous results growing modes are found for each value of the applied current.