Database

[{_id:"000000000000000000001001",MyIntArray:[10,15],MyStringArray:["square","box"]},{_id:"000000000000000000001002",MyIntArray:[22,27],MyStringArray:["round","ball"]}]

Query

db.collection.update({_id:"000000000000000000001002",MyStringArray:"round"},{$set:{"MyStringArray.$":"triangle"}})

Result