The problem of the spread of contamination by seepage is solved by optimizing the shape of the channel bed for the objective function -- the particle travel time along a streamline with integral constraints, the flow rate and cross-sectional area of the reservoir. The problem can be reduced to the solution of Dirichlet's problem by means of an integral representation of the required analytic function, series expansionof the kernel of the Cauchy integral and the determination of the coefficients of the series from the extremum condition.