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In this article, a new approach is described that enables the reduction of noise artifacts in elastography without a significant reduction in either the contrast or spatial resolution. The technique uses angular weighted compounding of local angular strains estimated from echo signals scanned at different insonification angles. Strain estimated along angular insonification directions can be separated into strain tensor components along the axial (direction of compression) and lateral directions. The mechanical stimulus is applied only along one direction. Angular weighting factors are derived from the relationship between the axial and lateral strains under the assumption of tissue incompressibility. Experimental results using a uniformly elastic tissue-mimicking phantom demonstrate the improvement in the SNRe obtained with angular weighted compounding. Variation in the SNRe obtained using different angular increments is also investigated. Elastograms obtained from an inclusion phantom also demonstrate the improvement in contrast detail resolution.