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We present a numerical method for solving Weyl's embedding problem which consists of finding a global isometric embedding of a positively curved and positive-definite spherical 2-metric into the Euclidean three space. The method is based on a construction introduced by Weingarten and was used in Nirenberg's proof of Weyl's conjecture. The target embedding results as the endpoint of an embedding flow in R^3 beginning at the unit sphere's embedding. We employ spectral methods to handle functionsdoi:10.1088/0264-9381/29/15/155010 fatcat:rqccblrqxvfbhanlcyydorq4oq