The well-known multiplicative decomposition(MD)model pioneered by Rodriguez et al.[1] has been widely employed for predicting residual stresses and morphologies of biological tissues due to growth.However,it relies significantly on the assumption that the tissue is initially in a state of free stress,which conflicts with the fact that any growth state of a biological tissue is under a certain level of residual stresses that help to maintain its ideal mechanical conditions [2].Here,we propose a modified multiplicative decomposition(MMD)model in which the initial state(reference configuration)of a biological tissue bears a residual stress τ rather than stress free.The initial state is first transmitted to a virtual stressfree(VSF)state which releases theoretically the entire initially residual stress during which an initial elastic deformation F0 occurs.Then,the initial VSF state grows to another VSF state with a growth deformation Fg,and is further integrated to its practical configuration of a real tissue,resulting in an excessive elastic deformation Fe.With this decomposition,the total deformation of the tissue due to growth is expressed as F=Fe·Fg·F0,and the corresponding free energy density should be ψ≡ψ(τ,F).Key issues,including the explicit expression of the free energy density,the predetermination of the initial elastic deformation F0 and initially residual stress τ are addressed in this lecture.A tubular organ tissue is considered as a representative example to demonstrate the application of the proposed MMD model.Results suggest that the initially residual stress may poses significant influences on the growth stress and morphologies of biological tissues.More importantly,the MMD model bridges the gap between any two growth states of a biological tissue,each of which has a certain level of residual stresses.