Many twin models can be fitted using standard statistical software such as R, Stata and SAS, however you may also wish to consider the following for your analysis:

Add-ons specifically for family and twin analyses
mestreg (Stata)
Multivariate Event Times (mets) (R)
kinship2 (R)

Software specifically for family and twin analyses
Fisher¹ ²
Mendel³

General multilevel modelling software and add-ons
gllamm
MLwiN
PROC MIXED
Linear Mixed-Effects Models (lme)
Linear and Nonlinear Mixed Effects Models (nlme)
Stata mixed

Structural equation modelling
OpenMx
Mplus

1. Hopper, J.L. & Mathews, J. A. (1994). Multivariate Normal Model For Pedigree And Longitudinal Data And The Software 'Fisher. Australian & New Zealand Journal of Statistics, 36(2): 153-76.
2. Lange, K., Weeks, D., & Boehnke, M. (1988). Programs For Pedigree Analysis: MENDEL, FISHER and dGene. Genetic Epidemiology, 5: 471-2.
3. Lange, K., Papp, J.C., Sinsheimer, J.S., Sripracha, R., Zhou, H., & Sobel, E.M. (2013). Mendel: The Swiss Army Knife Of Genetic Analysis Programs. Bioinformatics, 29 (12):1568-70.