Molecular self-assembly is becoming an increasingly popular route to new supramolecular structures and molecular materials. The inspiration for such structures is commonly derived from self-assembling systems in biology. Here we show that a biological motif, the peptide beta-sheet, can be exploited in designed oligopeptides that self-assemble into polymeric tapes and with potentially useful mechanical properties. We describe the construction of oligopeptides, rationally designed or based on segments of native proteins, that aggregate in suitable solvents into long, semi-flexible beta-sheet tapes. These become entangled even at low volume fractions to form gels whose viscoelastic properties can be controlled by chemical (pH) or physical (shear) influences. We suggest that it should be possible to engineer a wide range of properties in these gels by appropriate choice of the peptide primary structure.