General purpose SEM software, such as OpenMx, lavaan (both open source packages based in R), AMOS, Mplus, LISREL, or EQS among others may be used to estimate growth trajectories.
A special topic of interest is the correlation of the growth parameters, the so-called initial status and growth rate, as well as their relation with time varying and time invariant covariates.
Models with higher order components, e.g., quadratic, cubic, do not predict ever-increasing variance, but require more than two occasions of measurement.
Though straightforward to fit with versatile software such as OpenMx, these more complex models cannot be fitted with SEM packages in which path coefficients are restricted to being simple constants or free parameters, and cannot be functions of free parameters and data.
Discontinuous models where the growth pattern changes around a time point (for example, is different before and after an event) can also be fit in SEM software.