Abstract--Precise prediction of electrical contact resistance is important for microswitches. The contact spot used to be considered as a circle in earlier literature, where there was only one geometrical parameter: the radius of the a-spots. However, a real contact asperity has a height and an angle with the interface. In this paper, a 3-dimensional cone-truncated geometry is used to model an asperity, and three parameters are defined: radius, height and the angle of the side with respect to the surface plane. The ranges of their values are extracted from AFM easurement of samples in Au and Ru, and the values match well with the previous mechanical simulation results. Compared to the theoretical results, the finite element (FE) model showed a good capability to predict contact resistance in the diffusive regime, but underestimated it in the ballistic regime. The effects of angle and height of the asperity were investigated for Au-Ru contact in terms of contact resistance, maximum temperature and its location. Regarding multiple spots in contact, this work investigated the influence of the number of spots and their distributions for contact resistance and local Joule heating.