Abstract: In order to solve the disadvantage of conventional step-type structural optimization,a unified optimization method which can carry out the structural topology,shape and sizing optimization concurrently is presented to realize the structural optimization for continuum structures.The unified structural optimization model and the structural geometry boundary are described with the level set function,by applying the compactly supported radial basis function with favorable smoothness and accuracy to interpolate it.The expansion coefficients of interpolants are regarded as the design variables which reflect the structural performance impacts of topology,shape and size.Accordingly,the original topology,shape and sizing optimization is now fully transformed into a relatively simple parameterization problem,namely,sizing optimization with the expansion coefficients of interpolants as a limited number of design variables.As a result,some efficient and matured optimization algorithms can be applied to improve the efficiency of optimization.Furthermore,the unified optimization model is constructed with the R function.Typical examples demonstrate that the method has achieved the unified optimization of continuum structures,with good efficiency and accuracy.