A robust simian-human immunodeficiency virus (SHIV)-macaque model of latency is critical to investigate eradicative and suppressive strategies that target HIV-1 Env. To this end, we previously reported a novel strategy for constructing SHIVs that bear primary or transmitted/founder (TF) Envs with modifications at Env residue 375 that enable efficient replication in Indian rhesus macaques (RM). Such TF SHIVs, however, have not been examined for their suitability for HIV-1 latency and cure research. Here, we evaluate two promising TF SHIVs, SHIV.D.191859 and SHIV.C.CH848, which encode TF subtype D and C HIV-1 Envs, respectively, for their viral kinetics and persistence during suppressive combination antiretroviral therapy (cART) and treatment interruption in RM. Our results suggest that the viral kinetics of these SHIVs in RM during acute, early, and chronic infection, and upon cART initiation, maintenance and discontinuation, mirror those of HIV-1 infection. We demonstrate consistent early peak and set point viremia, rapid declines in viremia to undetectable plasma titers following cART initiation, infection of long-lived cellular subsets and establishment of viral latency, and viral rebound with return to pretreatment set point viremia following treatment interruption. The viral dynamics and reservoir biology of SHIV.D.191859, and to a lesser extent SHIV.C.CH848, during chronic infection, cART administration, and upon treatment interruption suggest that these TF SHIVs are promising reagents for a SHIV model of HIV-1 latency and cure.IMPORTANCE Simian-human immunodeficiency viruses (SHIVs) have been successfully used for over 2 decades to study virus-host interactions, transmission, and pathogenesis in rhesus macaques. The majority of Env trimers of most previously studied SHIVs, however, do not recapitulate key properties of transmitted/founder (TF) or primary HIV-1 isolates, such as CCR5 tropism, tier 2 neutralization resistance, and native trimer conformation. Here, we test two recently generated TF SHIVs, SHIV.D.191859 and SHIV.C.CH848, which were designed to address these issues as components of a nonhuman primate model of HIV-1 latency. We conclude that the TF SHIV-macaque model reflects several hallmarks of HIV and SIV infection and latency. Results suggest that this model has broad applications for evaluating eradicative and suppressive strategies against the HIV reservoir, including Env-specific interventions, therapeutic vaccines, and engineered T cells.