Abstract: A test of 3-dimensional multivariate optimum interpolation has been performed in a regional analysis. The domain covering (20°N-60°N,75°E-140°E) over eastern Asia is chosen for the test which is divided into 66 boxes of 660×660 km2. Three variates, geopotential height(φ),zonal and meridional compo- nents of wind (u and v) are analysed for the 500 hPa and 300 hPa levels. Based on the formula of error covariances in spherical coordinates the programme of automatic data quality control and analysis have been set up and the analysis increments and interpolation error evaluated. Some mathematical problems involved in OI are discussed concentrating on the characteristies of the error covariance. matrix M. Two methods to modify the M matrix are suggested when its positive definite property violated to ensure the success of OI analysis.