This thesis concentrates on mini-fracture propagation and closure, providing an innovative way to analyze this process. Source and sink function is implemented as a theoretical foundation to build the modeling strategy. A robust model is successfully developed to investigate fracture propagation by taking initial formation breakdown pressure, expansion of wellbore fluid after fracture initiation into consideration, which have always been ignored in literature by former researchers. Using injecting rate as the reference rate, dimensionless fracturing fluid leak-off rate normally described as flux term can be effectively coupled when source and sink function method is implemented. The dimensionless fracture volume growing rate during injection can be explicitly revealed through establishing the material balance equation among the injection fluid, wellbore fluid expansion and fluid leak-off. For shut-in period, the ultimate fracture half-length at shut-in can be found by diagnosing pressure data during injection and coupling with pressure decline during closure period, adding more confidence to the results analyzed. Type curves are documented with sensitivity analysis including fracture propagating velocity, wellbore storage effect, formation breakdown pressure, and injecting rate. It is observed that higher fracture propagating velocity in length results in larger ultimate fracture volume. When fluid expansion in wellbore is considered, larger fracture volume is created and more fluid leakage into reservoir is happening, suggesting that fracturing fluid with larger compressibility or wellbore with larger volume can help hold up the bottom hole pressure from falling and contribute further to incremental fracture volume. When fracturing fluid inside wellbore is compressed to reach a higher formation breakdown pressure level before fracture initiation, faster well bottom pressure decline and more fluid expansion from wellbore fluid occur, creating less fracture volume in mini-fracturing process. At wellhead, smaller injecting rate leads to faster bottom hole pressure decline, less fracture volume but more fluid volume leakage into reservoir. Mini-fracture or DFIT analysis for the inference of fracturing fluid leak-off volume, fracture length and width is the main targeting application of this study. Moreover, it is capable of analyzing post-fracture performance with variable conductivity like fracture geometry change, and providing a base for hydraulic fracturing design.