Yes, in fact there are many accounts by Soviet armed forces members themselves which either heavily insinuate or directly claim that such rapes did occur.
The best account material is from Vasily Grossman, in his book "Writer at War". Grossman was with the front line units of the 8th Guards Army as a journalist and would've seen such acts first hand. He mentions, in three different accounts:
Horror in the eyes of women and girls [sic]....Horrifying things are happening to German women. An educated German explains to us in gestures and broken German that his wife has been raped by 10 men already today. Women's screams are heard from open windows.
A young Frenchman said to me: "Monsieur, I love your army and that's why it is painful for me to see its attitude to girls and women. It is going to be very harmful for your propaganda".
There are many young women crying in the streets [of Berlin]. Apparently many have been made to suffer at the hands of our soldiers.
It seems that some Soviet women were not spared, either
Soviet girls liberated from camps are suffering a lot now. During the night, we are woken up by screams; one of the correspondents couldn't resist the temptation. A noisy discussion ensues, but then order is restored.
There are no controversies on Grossman's journalistic integrity. He reported faithfully the heroic defense of Stalingrad and was regarded as a hero.
It appears that Grossman is not alone in this. Tank Commander Vasiliy Krysov was in East Prussia with his T-34. I sadly do not have the book with me anymore (I found the translation hard to read and threw it away) but I remember what he wrote. Regardless, I took this from a review from Amazon, and it corroborates what I remembered:
...he tells us a story of how three soldiers from his unit raped a twelve year old German girl and got no punishment. He does not think this was right but also comments that they were spared because the Germans used to rape Russian women and girls too. Apparently he does not reflect on the fact that they then ended up being equally bad.
Krysov also states that "I refused to rape because of moral principles". This statement clearly indicates that a lot more took place than the isolated case he reports.
Nikolai Safinov, Infantryman in the 110th Rifle Division, writes for the 'IRemember.ru' site:
There were also cases of raping German women. I remember a widely known fact of a group rape when 33 soldiers raped a German woman. There were talks that after that news reached General Kotikov, the chief of the Political Department of the 61st Army, he shook his head especially wondering at those who were at the tail end of the line of rapists. Nevertheless, that criminal case had been dropped.
Finally, Yurii Koriakin, Rifleman in the 10th Guards Rifle Division, recalls a politburo officer telling him:
"Well, and concerning the woman question, you can treat the German
women rather freely, but so it wouldn't look organized. 1-2 men can
go, do what they need (that's exactly what he said: "what they need"),
return, and that's all. Any kind of pointless damage to German men and
women is inadmissible and will be punished."
This conversation made us feel that he himself didn't know exactly
what norms of behavior should've been followed. Of course, we were all
under the influence of propaganda, which didn't differentiate Germans
and Hitlerites in those times. That's why I know of a ton of cases
when German women were raped, but not killed. Treatment of German
women (we almost never saw men) was free, even vengeful. In our
regiment the Sergeant Major of the supply company set up practically
an entire harem.
Svetlana Alexivich in her book also states:
When we occupied every town, we had first three days for looting and ... [rapes]. That was unofficial of course.
As you can see, there are many sources by Russians themselves which corroborate Beevor's claim.
Obviously no Soviet soldier in their right mind would broadcast out loud the atrocities happening, either because they didn't know what was happening on other fronts or, if they were high enough to know, they would be immediately prosecuted for speaking against the state as was the case of Grossman. But as is evident on this website, the Soviet propaganda machine is still largely intact and there are plenty of narrow-minded kleptons who will readily deny Soviet atrocities in the Second World War, no different to Nazi holocaust deniers or Japanese Nanking deniers.