Aims. We investigate the influence of metallicity and stellar wind mass loss on the radius of Wolf-Rayet stars. Methods. We have calculated chemically homogeneous models of Wolf-Rayet stars of 10 to 200 M for two metallicities (Z = 0.02 and Z = 0.001), without mass loss, using OPAL opacities. We also constructed theoretical helium main sequences for 15, 18, 24 and 30 M with stellar wind mass loss rates of 10 −5 M yr −1 and 10 −4 M yr −1 and models for a 24 M star for a few intermediate values

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... mass loss rate. Results. We confirm the radius extension for luminous, metal-rich Wolf-Rayet stars reported previously by Ishii et al. (1999, PASJ, 51, 417), i.e. the inflation of the hydrostatic stellar radius. We also show that for small values of the stellar wind mass loss rate, an extended envelope structure is still present. However, for mass loss rates above a critical value, for which we derive an expression, Wolf-Rayet radii decrease and the stellar structure becomes compact. We briefly discuss possible evolutionary and observational consequences of an inflated envelope for a mass losing Wolf-Rayet star. Article published by EDP Sciences and available at http://www.edpsciences.org/aa or http://dx.