If dark matter has a finite size, the related physics will be changed and different direct detectional signal s are given. In this report, we will focus on the self-interacting puffy dark matter scenario and the direct dectection of finite–size dark matter via electro recoil and cosmic ray acceleration. In light of self-interacting puffy dark matter, we firstly consider that the intrinsic interaction responsible for the structure formation is inevitable from the perspective of dark matter self-scattering. The Chou-Yang model is then introduced to reduce the number of input parameters to one based on the simplicity and analyticity principle. Even in the absence of the dark strong interactions, revisiting puffy dark matter with novel insights: partial wave analysis are shown. For such puffy DM self-interaction cross-section in the resonant and classical regimes, our study demonstrates the significance of the Yukawa potential and the necessity of partial wave analysis. Then, we find out two new parameters to classify the self-scattering cross section into the Born, the resonance and the classical regimes for the puffy dark matter. And we examine the Sommerfeld enhancement effect for the puffy self-interacting dark matter. Finally, the direct dectection of finite–size dark matter gave the different results than particle-like dark matter.