We present an analytic approach to the estimation of beam asymmetry effects in cosmic microwave background (CMB) temperature and linear polarization anisotropy experiments. We derive via perturbative expansions simple and accurate results for the case of an elliptical Gaussian window. Our results are applied to investigate the effect of beam ellipticity in the estimation of full-sky polarization correlation functions and the covariance matrix of power spectra. The relevance of this effect is also discussed by forecasting errors including beam asymmetry for current and future cosmic microwave background (CMB) experiments.