Depending on the processing conditions, isotactic Polypropylene (iPP) can form different crystalline phases, Injection molding samples show a distribution of four different phases (α, β, γ, meso) over the thickness of the sample. However, a key issue in studying the crystallization process of semi-crystalline polymers is the need for controlled boundary and initial conditions; injection molding does not meet these requirements. Here, the results of extended dilatometry are used to reveal the crystallization kinetics and the resulting morphology of an isotactic polypropylene homo-polymer resulting from a combination of non-isothermal cooling at elevated (isobaric) pressures and shear flow. Based on the flow strength, defined in terms of the Weissenberg number, the crystallization kinetics can be classified in three regimes; quiescent crystallization, flow enhanced point nucleation and flow-induced creation of oriented structures. Using ex-situ WAXD and SAXS the details of the (oriented) crystalline structures for the different regimes, including the different phases (α, β, γ), are revealed. Some unique oriented structures of combined α- and γ-phase were found. We developed a model in terms of a set of rate equations for the different phases, which are partially coupled. The most important ingredients of the model are: - Flow creates nuclei and shish-kebabs - Fixed portion of flow-induced nuclei is assigned to the β-phase (~0.2%), the rest is assigned to α/γ according to their momentary crystal growth rate - Shish form parents and daughters - Parameters for crystal growth rates for all phases are taken from literature. - There are two limiting cases for the γ-phase; daughters grow on α-kebab only or - γ-phase can grow on shish as parents as well as daughters on α-kebab Combining a known nucleation model with a known multi-phase model gives qualitative agreement with experiments. To our knowledge, this is the first time that such an extended modeling is presented.