Matched‐field processing techniques can be both ambiguity‐prone and sensitive to errors in the assumed environmental conditions. Although greater robustness to environmental variability can be obtained by the use of data adaptive methods, such as the MV‐EPC beamformer [J. L. Krolik, J. Acoust. Soc. Am. 92, 1408–1419 (1992)] or joint estimation of source and channel parameters [D. F. Gingras and P. Gersoft, J. Acoust. Soc. Am. 97, 3589–3598 (1995)], these strategies require higher signal‐to‐noise ratios. The methods presented here concern the design of robust nonadaptive beamformer weights with sidelobe levels which are less signal‐to‐noise ratio dependent. As with Chebyshev filters, the weights are designed to minimize the maximum magnitude‐squared sidelobe level. Robustness to environmental mismatch is achieved by defining the sidelobe level as the magnitude‐squared response averaged over an ensemble of environmental conditions. The two algorithms proposed are a fast iterative constrained minimum variance method and the use of a minimax quadratic programming technique. For an uncertain Mediterranean environment, an improvement in the maximum average sidelobe level of as much as 3 dB over the Bartlett beamformer is achieved. [Work supported by NRaD/ONR.]