There are both common and rare genetic causes for kidney stones. 

Hypercalciuria:  One of the most common causes of kidney stones is hypercalciuria. In this condition, the urine has excessively high levels of calcium.  Analysis of family members with and without stones demonstrates that this trait (i.e. elevated urinary calcium concentrations) is passed from generation to generation. There are likely several causes for hypercalciuria and therefore probably different genes involved. Since the majority of people with calcium kidney stones have hypercalciuria, this is one of the most common genetic defect(s) to cause disease.

Hyperoxaluria:  This genetic disorder presents often during childhood. There are two genetic defects known to cause high urinary oxalate levels which can cause kidney stones to be present at a young age. In Type I primary hyperoxaluria there is a deficiency of alanine glyoxylate aminotransferase. Often there is deposition of calcium oxalate throughout the body. In Type II disease the deficiency is D-glyceric dehydrogenase. Treatment sometimes involves liver (plus or minus) kidney transplant. If a liver transplant is necessary, hopefully this is performed prior to significant damage occurring to the kidneys. Otherwise, a double transplant maybe necessary.

Cystinuria:  This genetic disorder leads in increased urinary cystine concentrations.  It accounts for 1-2% of kidney stones.  It is discussed in depth on the Cystine Kidney Stone Page.

Polycystic Kidney Disease:  Polycystic kidney disease is a genetic disorder in which multiple cysts/blisters form in the kidney.  It can develop at different ages depending on the genetic mutation.  The causes of stone formation in this disease are not completely understood, but may include decreased urine flow in the cystic areas and low urine citrate concentrations.

Distal Renal Tubular Acidosis (RTA):  RTA (renal tubular acidosis) refers to an inability to excrete acid into the urine which is a normal function of the kidneys.  Each day through eating, especially protein, people consume acid which must be excreted into the urine. In certain diseases, particularly autoimmune disorders such as Sjogren's syndrome or primary biliary cirrhosis, kidney damage can occur that prevents the kidney from excreting acid.  In other people an RTA is a genetic disorder.  In people with an RTA, calcium stones, particularly calcium phoshate can precipitate. Certain genetic forms can be associated with rickets, hearing loss, and nephrocalcinosis (calcium deposition in the kidney).

Hyperparathyroidism:  Hyperparathyroidism causes elevated blood calcium levels which can lead to elevated urine calcium levels and kidney stones. This is usually not agenetic disorder. However, there is a rare genetic disease known as multiendocrine neoplasm (MEN) which can be
associated with hyperparathyroidism, kidney stones, and
other endocrine organ abnormalities. 

Uric Acid Stones:  Hypoxanthine-guanine phosphoribosyltransferase enzyme deficiency which is sometimes associate with Lesch Nyhan syndrome causes elevated uric acid levels and stones. A range of diseases
associated with different degrees of enzyme deficiency
occur.