If I jump off of the roof of 30-storey building holding an open
umbrella, will it work like a parachute?

Hello there

Regardless of how large the umbrella was, you would fall rapidly.

An umbrella has a "hinged" canopy support while a parachute has a
"shrouded" support.

In other words, the way umbrellas are designed, when too much wind
hits them from beneath, they turn "inside out."  Whatever hinging
mechanism is used, it connects somewhere in mid-canopy allowing this
inside-out action to take place.

A parachute on the other hand has shrouds (lines) connected to the
outer rim of the canopy preventing it from turning "inside out." 
Regardless of how much air pushes up beneath it, the shrouds hold the
edges down.

An umbrella a 100 feet across would still give you a hard landing
while a relatively small parachute can get you down safely.

Please notice I did not take the height of the building into account. 
A 30 story (roughly 300 foot drop) may not be long enough for a chute
to open in the first place.

Cheers
Digs

sweet.

An umbrella would have to be improbably huge in order to function as a
parachute for a human being. Consider that the canopy of a
BASE-jumping parachute is around 200 square feet in area. Have you
ever seen an umbrella that was anywhere near that size? I don't think
so.

Even if the umbrella were sufficiently large, it would almost
certainly be yanked from your hand shortly after you began your
descent.

Great answer, Digs! In fretting about the small size of the umbrella,
I quite ignored its critical structural difference from a parachute.

Even if you were to build an umbrella both big enough and strong
enough you'd still have a hard landing.  A circular parachute has a
central vent to stop it rocking - an umbrella doesn't, so it will
side-slip and come down faster. You, hanging on to the handle, will be
swinging around all over the place, so  you're in for a rough ride as
well.

Ian G.

I tested this directly as a youngster by jumping off the back porch
steps, probably about 8 or 10 feet off the ground.  I was a skinny
little kid and couldn't have weighed more than about 60 lb. at the
time.  In that short distance, no matter how hard I held onto the
umbrella handle and tried to keep it vertical, it twisted in my hand
and wouldn't hold the position it had to to act like a parachute.  It
tipped over and dropped me, and I landed pretty hard.

Nevertheless, I kept trying it until I had bashed up my mother's
umbrella pretty well.  I have to tell you also that I was wearing one
of her silk scarves as a cape to aid the effect of flying that I hoped
to achieve, and that didn't actually help much either.

So I wouldn't recommend trying this from 30 stories.

Archae0pteryx