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A method is developed to calculate exciton parameters in an arbitrarily shaped quantum well by using numerical methods in conjunction with the variational method. We solve the Schrödinger equation of the relevant system both by the Monte Carlo method and by the ordinary differential equation solving method, and find that the two approaches yield similar results. Our technique is readily applied to arbitrarily shaped GaAs/AlGaAs quantum wells, and allows us to study the variation of exciton parameters with respect to transverse electric field. We report the results for exciton binding energies, electron and hole tunneling rates, and exciton volumes, which are essential to predicting electro‐optical properties of quantum well. Results are presented for the square, graded, and asymmetric quantum wells, and the effects of the shape of the well on exciton properties are discussed. We find that there is only small dependence of the exciton binding and emission energy on the well shape, but a strong dependence of the electron and hole tunneling rates and hence of the dynamical aspects of excitonic properties on the well shape.