Univariate P\'olya basis is extended to bivariate basis for triangular patchs modeling. These patches are called P\'olya triangular patches. P\'olya triangular patch is shown to be the generalization of Bernstein-B\'ezier triangular patch. They are also shown to have many properties desirable for CAGD; in particular they are affine invariant, possess a recursive evaluation algorithm. Further , these patches have shape parameters which may be used as a design tool for introducing such geometric effects as tautness or approximation.