The rheology of the lithosphere determines its deformation under given
initial and boundary conditions. This paper presents a critical discu
ssion on how rheological properties are taken into account in extensio
nal basin modelling. Since strength envelopes are often used in models
, we review the uncertainties (in temperature and rheological paramete
rs) and assumptions (in type of rheology and mode of deformation) invo
lved in their construction. Models of extensional basins are classifie
d into three groups: kinematic, kinematic with rheological constraints
, and dynamic. Rheology enters kinematic models only implicitly, in th
e assumption of an isostatic compensation mechanism. We show that ther
e is a critical level of necking that reconciles local isostasy with t
he finite strength of the lithosphere, which requires a flexural respo
nse. Kinematic models with rheological constraints make use of strengt
h envelopes to assess the initial lateral variations of lithospheric s
trength and its evolution with time at the site of extension. Dynamic
models are the only ones to explicitly introduce rheological constitut
ive equations (usually in plane strain or plane stress). They usually,
however, require the presence of an initial perturbation (thickness v
ariations, pre-existing faults, thermal inhomogeneities, rheological i
nhomogeneities). The mechanical boundary conditions (kinematic and dyn
amic) and the thermal boundary conditions (constant temperature or con
stant heat flux at the lower boundary of the lithosphere) may result i
n negative/positive feedbacks leading to cessation/acceleration of ext
ension. We conclude that, while kinematic models (with rheological con
straints if possible) are very successful in accounting for the observ
ed characteristics of sedimentary basins, dynamic models are necessary
to gain insight into the physical processes underlying basin formatio
n and evolution.