Conventional ultrasound strain imaging usually only calculates the axial strain. Although axial strain is the main component of two dimensional strain field, lateral displacement and strain estimation can provide additional information of human mechanical properties. Shear strain andPoisson’s ratio can be estimated by using lateral strain estimation technique. Low lateral sampling rate and decorrelation noise of lateral radio frequency (RF signal caused by axial displacement motion increase the difficulty of lateral strain estimation. Subband division techniqueis to divide a broadband signal into several narrowband signals. In this paper, the application of subband division technique in axial and lateral strain estimation is studied, and an iterative method for estimating axial and... lateral strains is proposed based on subband technique. The subbanddivision of this method is carried out along the axial direction, so that the bandwidth of the lateral subband signal is maintained and the quality of the lateral sub strain image is not reduced. In this paper, the number of subbands is three; the compounded lateral strain image is obtainedby superimposing these sub strain images on the average. In each iteration, the temporal stretching technique is used to align the axial and lateral RF signals by using the axial and lateral displacement estimation information, which reduces the decorrelation noise of the RF signals. The lengthof temporal stretching window decreases with the number of iterations, so as to gradually improve the accuracy of temporal stretching. The phase zero algorithm is used to estimate the axial and lateral displacements. The effectiveness of this method is tested by simulations. The simulationresults show that the elastographic signal-to-noise ratio (SNRe of lateral strain image is increased by about 50%, the elastographic contrast noise ratio (CNRe of lateral strain image is increased by about 120%, the SNRe of axial strain image is increased by about 4%, the CNRe of axial strainimage is increased by 8%, and the signal-to-noise ratio of Poisson’s ratio image is increased by about 40%.