A new computational approach (PEP) is presented for the structure-based design of linear polymeric ligands consisting of any type of amino acid. Ligands are grown from a seed by iteratively adding amino acids to the growing construct. The search in chemical space is performed by a build-up approach which employs all of the residues of a user-defined library. At every growing step, a genetic algorithm is used for conformational optimization of the last added monomer inside the binding site of a rigid target protein. The binding energy with electrostatic solvation is evaluated to select sequences for further growing. PEP is tested on the peptide substrate binding site of the insulin receptor tyrosine kinase and farnesyltransferase. In both test cases, the peptides designed by PEP correspond to the sequence motifs of known substrates. For tyrosine kinase, tyrosine residues are suggested at position P and P+2. While the tyrosine at P is in agreement with the experimental data, the one at P+2 is a prediction which awaits experimental validation. For farnesyltransferase, it is shown that electrostatic solvation is necessary for the correct design of peptidic inhibitors.