At the macroscopic scale, concrete appears as a composite made of a cement paste matrix with embedded aggregates. The latter are covered by interfacial transition zones (ITZs) of reduced stiffness and strength. Cracking in the ITZs is probably the key to the nonlinear stress–strain behavior in the prepeak regime. For a deeper understanding of this effect triggered by tensile microstress peaks, we here employ and extend the framework of continuum micromechanics, as to develop analytical solutions relating the macroscopic stresses acting on a piece of concrete, to microtractions at the aggregates' surfaces and to three-dimensional stress states within the ITZs. In the latter context, a new aggregate-to-ITZ stress concentration tensor is derived based on the separation-of-scale principle, which implies that ITZs may be modeled as two-dimensional interfaces at the concrete scale, but as three-dimensional bulk phases at the scale of a few micrometers. Microtensile peaks occur both under uniaxial macroscopic tension and compression. To describe the respective microtraction and microstress fields, it is suitable to define aggregate's “poles” and “equator” by an “axis” through the aggregate center, directed in the uniaxial macroscopic loading direction. Accordingly, tensile microtraction peaks, induced by macro-tension and macro-compression, respectively, occur at the “poles” and at the “equator”, respectively. The largest tensile ITZ-microstresses occur at an offset of about π/8 from the “poles” and the “equator”, respectively. These fields of microtractions and ITZ microstresses are prerequisites for upscaling ITZ-related strength to the macroscopic concrete level, as presented in the companion paper (Part II).