Mass movements such as debris flows and landslide differ in behavior due to their material properties and internal forces. Models employ generalized multi-phase flow equations to adaptively describe these complex flow types. However, models commonly assume unstructured and fragmented flow after initiation of movement. In this work, existing work on two-phase mass movement equations are extended to include a full stress-strain relationship that allows for runout of (semi-) structured fluid-solid masses. The work provides both the three-dimensional equations and depth-averaged simplifications. The equations are implemented in a hybrid Material Point Method (MPM) which allows for efficient simulation of stress-strain relationships on discrete smooth particles. Using this framework, the developed model is compared to several flume experiments of clay blocks impacting fixed obstacles. Here, both final deposit patterns and fractures compare well to simulations. Additionally, numerical tests are performed to showcase the range of dynamical behavior produced by the model. Important processes such as fracturing, fragmentation and fluid release are captured by the model. While this provides an important step towards complete mass movement models, several new opportunities arise such as ground-water flow descriptions and application to fragmenting mass movements and block-slides.