In gene mapping, after an initial genome-wide linkage scan, the next step often involves candidate region studies or fine mapping using dense markers. Dense genotyping, however, introduces linkage disequilibrium (LD). Traditional linkage analysis assuming no LD leads to increased false positive rates. Hence, we develop models to incorporate linkage disequilibrium, focusing on the sib pair design. Changes in sib-pair identity-by-descent (IBD) sharing along the chromosome can be modeled as a random walk. A hidden Markov model (HMM) framework is adopted to infer IBD sharing from genotypic data on sib pairs. In our first model, linkage equilibrium (LE) is assumed and only the IBD sharing is the hidden process. The effect of misspecification of allele frequencies is studied. We then use a first-order Markov model to incorporate LD into parental haplotypes and investigate the impact of linkage disequilibrium on IBD sharing estimation and lod score calculation. A cluster-based HMM developed by Scheet and Stephens  is then used to model LD in parental haplotypes, in order to capture better the LD patterns. However, parameter estimation for this cluster-based model is complicated. Moreover, at the dense mapping scales for which such models are appropriate, recombinant-based methods for linkage detection and estimation are impractical due to the low numbers of recombination events. Nonetheless, the hidden Markov model framework we have developed here provides a way to simulate genotypic data for related individuals with dense markers. It may also be useful in family-based association studies where this framework can be adopted to impute missing genotypes.