This thesis focuses on studying the rank of Selmer groups in quadratic twist families of elliptic curves over function field. Some of the results are closely related to Poonen-Rains heuristics that hypothesizes the average of Selmer ranks of elliptic curves in general. We show in the first part that if the quadratic twist family of a given elliptic curve over $\mathbb{F}_q[t]$ with no $\mathbb{F}_q(t)$-rational p-torsion points has an element whose Neron model has a multiplication reduction away from $\infty$, then the average $p$-Selmer rank is $p+1$ in large $q$-limit for almost all primes $p$. In the second part, we show that in the quadratic twist family of an elliptic curve over $\mathbb{F}_q[t]$ with a single point of order two that does not have a cyclic 4-isogeny defined over its two-division field, at least half of the quadratic twists have arbitrarily large 2-Selmer rank.