A novel adaptive high dimensional model representation (HDMR) is developed for stochastic finite element analysis of composite plate. Uncertainty propagating through the physical system is quantified using this technique where only the significant dimensions are retained. Influence of these dimensions is modeled by different orders which are preferred to be low for computational tractability. These dimensions are identified by a sensitivity analysis using support points in the sparse grid which are generated using multiple levels of hierarchy, joint or marginal probability distributions and dimension adaptiveness. This multi level hierarchical generation of support points fill the domain of the input variables with major emphasis on the regions of interest which may be the entire space, limit state, maxima/minima or tail ends of the probability distribution function for rare events depending upon the nature of the problem. The hybrid characteristics of the proposed dimension decomposition is introduced in this paper where the component functions are expressed using orthogonal bases and the error term which is further modeled using Gaussian random process (i.e. Kriging). The performance of the proposed Hybrid dimension adaptive HDMR (hdA-HDMR) is illustrated using stochastic finite element analysis of laminated composite plate whose material properties are considered as homogeneous non-normal random fields. © 2020 Elsevier Ltd