A ternary pentagonal form is a quadratic polynomial of the form f = f(x, y, z) = a(3x² − x)/2 + b(3y² − y)/2 + c(3z² − z)/2, where a, b and c are positive integers. We call f regular if, for every positive integer n, the equation f(x, y, z) = n has an integer solution if and only if it is solvable over the ring of p-adic integers ℤ_p for all primes p. By the works of Guy, Sun, Ge and Sun, and Oh, it is known that there are exactly 20 ternary pentagonal forms which represent all positive integers. In this talk, we show that there are at most 42 primitive regular ternary pentagonal forms and establish the regularity of 21 forms.