Interactive mesh editing techniques are commonly used for creating a new mesh model by deforming existing mesh models. In surface-based deformation, geometric shapes are encoded using differential equations, and they are deformed so that the equations and other constraints are satisfied in a least-squares sense. Although constraints are typically approximated as linear equations, constraints that preserve volume require nonlinear equations. In such cases, it is time-consuming to solve the nonlinear equations. In our method, we enclose a mesh model with multiple overlapping lattices so that a subset of vertices is shared by two or more lattices. Then, the vertex coordinates in equations are replaced by the coordinates of the lattices. Vertices shared by multiple lattices are used to propagate deformation between disconnected lattices. Our method makes it possible to efficiently solve non-linear equations and interactively deform mesh models while preserving the volume of mesh models.