Genetic imprinting, by which the expression of a gene depends on the parental origin of its alleles, may be subjected to reprogramming through each generation. Currently, such reprogramming is limited to qualitative description only, lacking more precise quantitative estimation for its extent, pattern and mechanism. Here, we present a computational framework for analyzing the magnitude of genetic imprinting and its transgenerational inheritance mode. This quantitative model is based on the breeding scheme of reciprocal backcrosses between reciprocal F(1) hybrids and original inbred parents, in which the transmission of genetic imprinting across generations can be tracked. We define a series of quantitative genetic parameters that describe the extent and transmission mode of genetic imprinting and further estimate and test these parameters within a genetic mapping framework using a new powerful computational algorithm. The model and algorithm described will enable geneticists to identify and map imprinted quantitative trait loci and dictate a comprehensive atlas of developmental and epigenetic mechanisms related to genetic imprinting. We illustrate the new discovery of the role of genetic imprinting in regulating hyperoxic acute lung injury survival time using a mouse reciprocal backcross design.