The mechanics for calculating the quantitative driving force of indentation-induced delamination of thin-film multilayers is presented. The solution is based on the mechanics developed by Marshall and Evans and extended to the general case of a multilayer by use of standard bending and thin-plate analyses. Presented and discussed are the specific solutions for the bilayer case that show that in the limit of zero thickness of either layer, the solution converges to the single-layer case. In the range of finite thickness, the presence of the superlayer increases the driving force relative to that possible for the original film alone and can be optimized to the experimental situation by proper choice of thickness, elastic constants, and residual stress. The companion paper `Quantitative adhesion measures of multilayer films: Part II. Indentation of W/Cu, W/W, Cr/W' discusses experimental results with copper, tungsten, and chromium thin films.