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Kinetic models of human motion rely on boundary conditions which are defined by the interaction of the body with its environment. In the simplest case, this interaction is limited to the foot contact with the ground and is given by the so called ground reaction force (GRF). A major challenge in the reconstruction of GRF from kinematic data is the double support phase, referring to the state with multiple ground contacts. In this case, the GRF prediction is not well defined. In this work we present an approach to reconstruct and distribute vertical GRF (vGRF) to each foot separately, using only kinematic data. We propose the biomechanically inspired force shadow method (FSM) to obtain a unique solution for any contact phase, including double support, of an arbitrary motion. We create a kinematic based function, model an anatomical foot shape and mimic the effect of hip muscle activations. We compare our estimations with the measurements of a Zebris pressure plate and obtain correlations of <inline-formula><math display="inline"><semantics><mrow><mn>0.39</mn><mo>≤</mo><mi>r</mi><mo>≤</mo><mn>0.94</mn></mrow></semantics></math></inline-formula> for double support motions and <inline-formula><math display="inline"><semantics><mrow><mn>0.83</mn><mo>≤</mo><mi>r</mi><mo>≤</mo><mn>0.87</mn></mrow></semantics></math></inline-formula> for a walking motion. The presented data is based on inertial human motion capture, showing the applicability for scenarios outside the laboratory. The proposed approach has low computational complexity and allows for online vGRF estimation.