We present a new deformation apparatus to model homogeneous deformation in general flow regimes, in which all combinations of simple shear parallel to the xy-plane and pure shear parallel to the x-, y-, and z-axes can be realized. With this apparatus it is possible to control the kinematic vorticity number of monoclinic flow during progressive deformation. The user defines the type of deformation by a set of parameters such as kinematic vorticity number, strain rate, and duration of the experiment. The apparatus consists of a set of mobile pistons on a low friction sole and is open at the top. All pistons are flexible to ensure homogeneity of deformation in a major part of the sample. The corners of the box are connected to four sliding carriages, which themselves are sliding on another set of four carriages positioned at right angles to the first set. This setup and the controlled movement of the sliding carriages allow the user to model any type of monoclinic transtension and transpression. A computer program controls six stepping motors used to move the different carriages simultaneously and accurately. In the apparatus materials with a viscosity range of 103to 106 Pa s can be used. Aset of pilot experiments investigating the rotation of mica fish in different general regimes is presented as an example for the use of this apparatus.