diff --git a/libavformat/rtpenc.c b/libavformat/rtpenc.c
index c9cea864eb..6fdc908d0f 100644
--- a/libavformat/rtpenc.c
+++ b/libavformat/rtpenc.c
@@ -262,7 +262,7 @@ fail:
 }
 
 /* send an rtcp sender report packet */
-static void rtcp_send_sr(AVFormatContext *s1, int64_t ntp_time)
+static void rtcp_send_sr(AVFormatContext *s1, int64_t ntp_time, int bye)
 {
     RTPMuxContext *s = s1->priv_data;
     uint32_t rtp_ts;
@@ -296,6 +296,13 @@ static void rtcp_send_sr(AVFormatContext *s1, int64_t ntp_time)
             avio_w8(s1->pb, 0);
     }
 
+    if (bye) {
+        avio_w8(s1->pb, (RTP_VERSION << 6) | 1);
+        avio_w8(s1->pb, RTCP_BYE);
+        avio_wb16(s1->pb, 1); /* length in words - 1 */
+        avio_wb32(s1->pb, s->ssrc);
+    }
+
     avio_flush(s1->pb);
 }
 
@@ -494,7 +501,7 @@ static int rtp_write_packet(AVFormatContext *s1, AVPacket *pkt)
     if ((s->first_packet || ((rtcp_bytes >= RTCP_SR_SIZE) &&
                             (ff_ntp_time() - s->last_rtcp_ntp_time > 5000000))) &&
         !(s->flags & FF_RTP_FLAG_SKIP_RTCP)) {
-        rtcp_send_sr(s1, ff_ntp_time());
+        rtcp_send_sr(s1, ff_ntp_time(), 0);
         s->last_octet_count = s->octet_count;
         s->first_packet = 0;
     }
@@ -590,6 +597,10 @@ static int rtp_write_trailer(AVFormatContext *s1)
 {
     RTPMuxContext *s = s1->priv_data;
 
+    /* If the caller closes and recreates ->pb, this might actually
+     * be NULL here even if it was successfully allocated at the start. */
+    if (s1->pb && (s->flags & FF_RTP_FLAG_SEND_BYE))
+        rtcp_send_sr(s1, ff_ntp_time(), 1);
     av_freep(&s->buf);
 
     return 0;
diff --git a/libavformat/rtpenc.h b/libavformat/rtpenc.h
index b0c9630ee9..913d05a73e 100644
--- a/libavformat/rtpenc.h
+++ b/libavformat/rtpenc.h
@@ -68,13 +68,15 @@ typedef struct RTPMuxContext RTPMuxContext;
 #define FF_RTP_FLAG_RFC2190   2
 #define FF_RTP_FLAG_SKIP_RTCP 4
 #define FF_RTP_FLAG_H264_MODE0 8
+#define FF_RTP_FLAG_SEND_BYE  16
 
 #define FF_RTP_FLAG_OPTS(ctx, fieldname) \
     { "rtpflags", "RTP muxer flags", offsetof(ctx, fieldname), AV_OPT_TYPE_FLAGS, {.i64 = 0}, INT_MIN, INT_MAX, AV_OPT_FLAG_ENCODING_PARAM, "rtpflags" }, \
     { "latm", "Use MP4A-LATM packetization instead of MPEG4-GENERIC for AAC", 0, AV_OPT_TYPE_CONST, {.i64 = FF_RTP_FLAG_MP4A_LATM}, INT_MIN, INT_MAX, AV_OPT_FLAG_ENCODING_PARAM, "rtpflags" }, \
     { "rfc2190", "Use RFC 2190 packetization instead of RFC 4629 for H.263", 0, AV_OPT_TYPE_CONST, {.i64 = FF_RTP_FLAG_RFC2190}, INT_MIN, INT_MAX, AV_OPT_FLAG_ENCODING_PARAM, "rtpflags" }, \
     { "skip_rtcp", "Don't send RTCP sender reports", 0, AV_OPT_TYPE_CONST, {.i64 = FF_RTP_FLAG_SKIP_RTCP}, INT_MIN, INT_MAX, AV_OPT_FLAG_ENCODING_PARAM, "rtpflags" }, \
-    { "h264_mode0", "Use mode 0 for H264 in RTP", 0, AV_OPT_TYPE_CONST, {.i64 = FF_RTP_FLAG_H264_MODE0}, INT_MIN, INT_MAX, AV_OPT_FLAG_ENCODING_PARAM, "rtpflags" } \
+    { "h264_mode0", "Use mode 0 for H264 in RTP", 0, AV_OPT_TYPE_CONST, {.i64 = FF_RTP_FLAG_H264_MODE0}, INT_MIN, INT_MAX, AV_OPT_FLAG_ENCODING_PARAM, "rtpflags" }, \
+    { "send_bye", "Send RTCP BYE packets when finishing", 0, AV_OPT_TYPE_CONST, {.i64 = FF_RTP_FLAG_SEND_BYE}, INT_MIN, INT_MAX, AV_OPT_FLAG_ENCODING_PARAM, "rtpflags" } \
 
 void ff_rtp_send_data(AVFormatContext *s1, const uint8_t *buf1, int len, int m);
 
diff --git a/libavformat/version.h b/libavformat/version.h
index 0bbc90cca3..f6329e4500 100644
--- a/libavformat/version.h
+++ b/libavformat/version.h
@@ -31,7 +31,7 @@
 
 #define LIBAVFORMAT_VERSION_MAJOR 55
 #define LIBAVFORMAT_VERSION_MINOR 20
-#define LIBAVFORMAT_VERSION_MICRO 104
+#define LIBAVFORMAT_VERSION_MICRO 105
 
 #define LIBAVFORMAT_VERSION_INT AV_VERSION_INT(LIBAVFORMAT_VERSION_MAJOR, \
                                                LIBAVFORMAT_VERSION_MINOR, \