  In this paper, using p-adic integration with values in spaces of modular
forms, we construct the p-adic analogue of Weil's elliptic functions according
to Eisenstein in the book "Elliptic functions according to Eisenstein and and
Kronecker". This construction extends Serre's p-adic family of Eisenstein
series in "Formes modulaires et fonctions z\^eta p-adiques". We show that the
power series expansion of Weil's elliptic functions also exists in the p-adic
case.
