With Scala's Set, is there a method analog to the containsAll method in Java's Set?

There is subsetOf, which tests whether or not the elements of a Set are contained within another Set. (Kind of the reverse in terms of the expression)

val set = Set(1,2,3,4)
val subset = Set(1,2)

scala> subset.subsetOf(set)
res0: Boolean = true

scala> set.subsetOf(subset)
res1: Boolean = false

In Scala, Set is equipped with set operations such as intersect, thus for instance

set.intersect(subset) == subset

conveys the semantics of containsAll, even that subsetOf as already mentioned proves the most succinct.

It's worth adding that you can make derived helper methods like containsAll available on Set[T] if you want, by using an implicit enriched class. You might also consider making a variadic overload:

implicit class RichSet[T](val x: Set[T]) extends AnyVal {
    def containsAll(y: Set[T]): Boolean = y.subsetOf(x)
    def containsAll(y: T*): Boolean = x.containsAll(y.toSet)
}

So then you can do:

Set(1, 2, 3).containsAll(Set(1, 2))

Or:

Set(1, 2, 3).containsAll(1, 2)